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Journal articles on the topic 'Bifurcation plot'

Author: Grafiati

Published: 5 June 2025

Last updated: 1 August 2025

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1

HU, JIAZHU, and P. FRANK PAI. "BIFURCATION STRUCTURE FOR MODULATED VIBRATION OF STRINGS SUBJECTED TO HARMONIC BOUNDARY EXCITATIONS." International Journal of Bifurcation and Chaos 21, no. 11 (2011): 3259–72. http://dx.doi.org/10.1142/s0218127411030507.

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In the studies of nonlinear dynamics, phase plan plot is a most commonly used tool for solution characteristics interpretation. Phase plan plot provides an adequate representation of the dynamic characteristics of single solution, but it does not provide information on the interrelation between neighboring solutions; therefore, the evolution of solutions is studied by examining fragmented information of many individual responses. When the solution space becomes complicated, accurate information of the interrelation between responses is essential for an overall comprehension of the characterist

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2

ORRELL, DAVID, and LEONARD A. SMITH. "VISUALIZING BIFURCATIONS IN HIGH DIMENSIONAL SYSTEMS: THE SPECTRAL BIFURCATION DIAGRAM." International Journal of Bifurcation and Chaos 13, no. 10 (2003): 3015–27. http://dx.doi.org/10.1142/s0218127403008387.

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This paper presents methods to visualize bifurcations in flows of nonlinear dynamical systems, using the Lorenz '96 systems as examples. Three techniques are considered; the first two, density and max/min diagrams, are analagous to the bifurcation diagrams used for maps, which indicate how the system's behavior changes with a control parameter. However the diagrams are generally harder to interpret than the corresponding diagrams of maps, due to the continuous nature of the flow. The third technique takes an alternative approach: by calculating the power spectrum at each value of the control p

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3

Biswas, Sujay, and Alaka Das. "Patterns, Bifurcations, Multistability and Hysteresis in an Inhomogeneous Coupled Map Lattice." International Journal of Bifurcation and Chaos 26, no. 03 (2016): 1630008. http://dx.doi.org/10.1142/s0218127416300081.

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We investigate local interaction between logistic maps in an inhomogeneous lattice numerically with respect to an inhomogeneity parameter [Formula: see text] and the coupling constant [Formula: see text]. In our model, the inhomogeneity appears in the form of different values of the map parameter at different sites. The phase diagram of the model in the [Formula: see text]–[Formula: see text] plane gives seven qualitatively different patterns. These are: synchronized patterns, steady (fixed in time) patterns with spatial period-two, spatially chaotic together with temporally periodic patterns,

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Saha, Asit, and Amiya Das. "Dynamical behavior of nonlinear wave solutions of the generalized Newell–Whitehead–Segel equation." International Journal of Modern Physics C 31, no. 04 (2020): 2050059. http://dx.doi.org/10.1142/s012918312050059x.

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Dynamical behavior of nonlinear wave solutions of the perturbed and unperturbed generalized Newell–Whitehead–Segel (GNWS) equation is studied via analytical and computational approaches for the first time in the literature. Bifurcation of phase portraits of the unperturbed GNWS equation is dispensed using phase plane analysis through symbolic computation and it shows stable oscillation of the traveling waves. Chaotic behavior of the perturbed GNWS equation is obtained by applying different computational tools, like phase plot, time series plot, Poincare section, bifurcation diagram and Lyapuno

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Güzel, İsmail, Elizabeth Munch, and Firas A. Khasawneh. "Detecting bifurcations in dynamical systems with CROCKER plots." Chaos: An Interdisciplinary Journal of Nonlinear Science 32, no. 9 (2022): 093111. http://dx.doi.org/10.1063/5.0102421.

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Existing tools for bifurcation detection from signals of dynamical systems typically are either limited to a special class of systems or they require carefully chosen input parameters and a significant expertise to interpret the results. Therefore, we describe an alternative method based on persistent homology—a tool from topological data analysis—that utilizes Betti numbers and CROCKER plots. Betti numbers are topological invariants of topological spaces, while the CROCKER plot is a coarsened but easy to visualize data representation of a one-parameter varying family of persistence barcodes.

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Rajagopal, Karthikeyan, Prakash Duraisamy, Riessom Weldegiorgis, and Anitha Karthikeyan. "Multistability in Horizontal Platform System with and without Time Delays." Shock and Vibration 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/1092812.

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Chaotic behavior and bifurcation analysis of horizontal platform systems (HPS) have been investigated widely by many researchers. However, the multistable features of such systems have not been investigated, and hence we identified the multistable parameter and investigated the coexisting attractors of the HPS. To understand the effects of time delays on the nonautonomous and autonomous HPS, we introduced a constant time delay in the state feedback variable. Investigation of the bifurcation of the time delayed HPS with time delay and parameters reveals that the system behavior differs between

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LI, QINGDU, XIAO-SONG YANG, and FANGYAN YANG. "HYPERCHAOS IN A SIMPLE CNN." International Journal of Bifurcation and Chaos 16, no. 08 (2006): 2453–57. http://dx.doi.org/10.1142/s0218127406016197.

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In this paper we demonstrate hyperchaotic dynamics in a very simple Cellular Neural Network (CNN) which is a one-dimensional regular array of four cells. The Lyapunov spectrum is calculated in a range of parameters, and the bifurcation plot is presented as well.

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Liu, Zeyu, Tiecheng Xia, and Jinbo Wang. "Image Encryption Technology Based on Fractional Two-Dimensional Triangle Function Combination Discrete Chaotic Map Coupled with Menezes-Vanstone Elliptic Curve Cryptosystem." Discrete Dynamics in Nature and Society 2018 (2018): 1–24. http://dx.doi.org/10.1155/2018/4585083.

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A new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference is proposed. We observe the bifurcation behaviors and draw the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits of the proposed map, respectively. On the application side, we apply the proposed discrete fractional map into image encryption with the secret keys ciphered by Menezes-Vanstone Elliptic Curve Cryptosystem (MVECC). Finally, the image encryption algorithm is analysed in four main aspects that indicate the proposed algor

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9

ZHENG, JIONGXUAN, JOSEPH D. SKUFCA, and ERIK M. BOLLT. "THE BUNDLE PLOT: EVOLUTION OF SYMBOLIC SPACE UNDER THE SYSTEM PARAMETER CHANGES." International Journal of Bifurcation and Chaos 23, no. 08 (2013): 1330028. http://dx.doi.org/10.1142/s0218127413300280.

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This paper provides a topological dynamics perspective on the full bifurcation unfolding in unimodal mappings. We present a bundle structure, visualized as a bundle plot, to show the evolution of symbolic space as we vary a system parameter. The bundle plot can be viewed as a limit process of an assignment plot, which are line assignments between points from two dynamical systems. Such line assignments are determined by a commuter, which is a coordinates transformation function that satisfies a commuting relationship but not necessarily a homeomorphism. The bundle structure is studied by under

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10

Zati Iwani Abdul Manaf, Nur Adiba Lyana Rosli, Nurul Aini Mahmood, and Noor Alia Yamin. "The Effect of Mosquito Biting Rate on the Malaria Transmission Model using Bifurcation Analysis." Journal of Mathematics and Computing Science 8, no. 1 (2022): 25–35. https://doi.org/10.24191/jmcs.v8i1.6972.

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This paper analyses a simple malaria transmission model to investigate the effect of parameter changes in mosquitoes per capita biting rate on human population, , by using the bifurcation analysis. For further investigation, we first formulated the malaria transmission model into a non-dimensionalized equation. Next, we employed the stability analysis of disease-free equilibrium and endemic equilibrium point of malaria transmission. Using the same non-dimensionalized equation, the one-parameter bifurcation analysis was conducted. A few graphs of the bifurcation diagram, phase plane and time se

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11

Saha, Asit. "Bifurcation analysis of the propagation of femtosecond pulses for the Triki-Biswas equation in monomode optical fibers." International Journal of Modern Physics B 33, no. 29 (2019): 1950346. http://dx.doi.org/10.1142/s0217979219503466.

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Bifurcation analysis of the propagation of femtosecond pulses for the Triki–Biswas (TB) equation in monomode optical fibers is reported for the first time. Bifurcation of phase plots of the dynamical system is dispensed using phase plane analysis through symbolic computation. It is observed that the TB equation supports femtosecond solitary pulse, periodic pulse, superperiodic pulse, kink and anti-kink pulses, which are presented through time series plot numerically. Analytical forms of the femtosecond solitary pulses are obtained. This contribution may be applicable to interpret the dynamical

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Rajagopal, Karthikeyan, Shirin Panahi, Anitha Karthikeyan, Ahmed Alsaedi, Viet-Thanh Pham, and Tasawar Hayat. "Some New Dissipative Chaotic Systems with Cyclic Symmetry." International Journal of Bifurcation and Chaos 28, no. 13 (2018): 1850164. http://dx.doi.org/10.1142/s021812741850164x.

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Designing new chaotic system with specific features is an interesting field in nonlinear dynamics. In this paper, some new chaotic systems with cyclic symmetry are proposed. In order to understand the overall behavior of such systems, the dynamical analyses such as stability analysis, bifurcation and Lyapunov exponent analysis are done. The accurate examination of bifurcation plot represents that these systems are multistable which makes them more interesting. Also, the basin of attraction of these systems is investigated to detect the type of attractors of these systems which are self-excited

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VIRGIN, L. N., J. M. NICHOLS, and S. T. TRICKEY. "A NOTE ON THE RESPONSE SPECTRUM MAP." International Journal of Bifurcation and Chaos 13, no. 05 (2003): 1337–41. http://dx.doi.org/10.1142/s0218127403007278.

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A plot of frequency, or spectral, content versus a system parameter was introduced in a recent paper by Billings and Boaghe [2001] as a useful alternative to bifurcation diagrams in nonlinear dynamics. The current contribution illustrates the same approach based on data taken from two experimental mechanical systems in which hysteresis is featured.

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HUANG, WEN-ZHI, and YAN HUANG. "CHAOS, BIFURCATION AND ROBUSTNESS OF A CLASS OF HOPFIELD NEURAL NETWORKS." International Journal of Bifurcation and Chaos 21, no. 03 (2011): 885–95. http://dx.doi.org/10.1142/s0218127411028866.

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Chaos, bifurcation and robustness of a new class of Hopfield neural networks are investigated. Numerical simulations show that the simple Hopfield neural networks can display chaotic attractors and limit cycles for different parameters. The Lyapunov exponents are calculated, the bifurcation plot and several important phase portraits are presented as well. By virtue of horseshoes theory in dynamical systems, rigorous computer-assisted verifications for chaotic behavior of the system with certain parameters are given, and here also presents a discussion on the robustness of the original system.

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15

Furter, J. E., and J. C. Eilbeck. "Analysis of bifurcations in reaction–diffusion systems with no-flux boundary conditions: the Sel'kov model." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 125, no. 2 (1995): 413–38. http://dx.doi.org/10.1017/s0308210500028109.

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A plot of the bifurcation diagram for a two-component reaction-diffusion equation with no-flux boundary conditions reveals an intricate web of competing stable and unstable states. By studying the one-dimensional Sel'kov model, we show how a mixture of local, global and numerical analysis can make sense of several aspects of this complex picture. The local bifurcation analysis, via the power of singularity theory, gives us a framework to work in. We can then fill in the details with numerical calculations, with the global analytic results fixing the outline of the solution set. Throughout, we

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Mamelak, Adam N., and J. Allan Hobson. "Dream Bizarreness as the Cognitive Correlate of Altered Neuronal Behavior in REM Sleep." Journal of Cognitive Neuroscience 1, no. 3 (1989): 201–22. http://dx.doi.org/10.1162/jocn.1989.1.3.201.

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Bizarreness is a cognitive feature common to REM sleep dreams, which can be easily measured. Because bizarreness is highly specific to dreaming, we propose that it is most likely brought about by changes in neuronal activity that are specific to REM sleep. At the level of the dream plot, bizarreness can be defined as either discontinuity or incongruity. In addition, the dreamer's thoughts about the plot may be logically deficient. We propose that dream bizarreness is the cognitive concomitant of two kinds of changes in neuronal dynamics during REM sleep. One is the disinhibition of forebrain n

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17

Dohnal, Josef. "The Plot of Leonid Andreevʼs “The Abyss” as a Bifurcation in a Literary Work?" Stephanos Peer reviewed multilanguage scientific journal 45, № 1 (2021): 23–29. http://dx.doi.org/10.24249/2309-9917-2021-45-1-23-29.

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The article analyses the development of the plot of the story by Leonid Andreev “The Abyss”, paying particular attention to the changes taking place in the internal structure of the “self” of the main character of the story, understood as a non-equilibrium system. A number of external impulses, initiated from the outside, causes gradually so powerful fluctuations that the character’s “self” undergoes a process of restructuring, which reveals until then hidden, unknown, primitive composite only partly overlaid by cultural memes.

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18

McCaughan, F. E. "Application of Bifurcation Theory to Axial Flow Compressor Instability." Journal of Turbomachinery 111, no. 4 (1989): 426–33. http://dx.doi.org/10.1115/1.3262290.

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When a compression system becomes unstable, the mode of response depends on the operating and system parameters, such as throttle setting and B parameter. Previous numerical work on the model developed by Moore and Greitzer has provided a limited picture of the parametric effects. Applying bifurcation theory to a single-harmonic version of the model has supplied much more complete information, defining the boundaries of each mode of response in the parameter space. Specifically this is shown in a plot of B versus throttle setting, which compares well with the corresponding map produced experim

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19

Rizwana, R., and I. Raja Mohamed. "Investigation of Chaotic and Strange Nonchaotic Phenomena in Nonautonomous Wien-Bridge Oscillator with Diode Nonlinearity." Journal of Nonlinear Dynamics 2015 (February 15, 2015): 1–7. http://dx.doi.org/10.1155/2015/612516.

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We have studied the chaotic and strange nonchaotic phenomena of a simple quasiperiodically forced Wien bridge oscillator circuit with diode as the only nonlinearity in this electronic oscillator system responsible for various nonlinear behaviors. Both the experimental results and the numerical simulation results for their confirmation are provided to show the bifurcation process. Various measures used for the numerical confirmation of SNA are power spectrum, maximal Lyapunov exponent, path of translational variables, mean square displacement, projection of poincaré section, log-log plot, and a

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20

Veeman, Dhinakaran, Hayder Natiq, Ahmed M. Ali Ali, Karthikeyan Rajagopal, and Iqtadar Hussain. "A Simple Conservative Chaotic Oscillator with Line of Equilibria: Bifurcation Plot, Basin Analysis, and Multistability." Complexity 2022 (March 26, 2022): 1–7. http://dx.doi.org/10.1155/2022/9345036.

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Here, a novel conservative chaotic oscillator is presented. Various dynamics of the oscillator are examined. Studying the dynamical properties of the oscillator reveals its unique behaviors. The oscillator is multistable with symmetric dynamics. Equilibrium points of the oscillator are investigated. Bifurcations, Lyapunov exponents (LEs), and the Poincare section of the oscillator’s dynamics are analyzed. Also, the oscillator is investigated from the viewpoint of initial conditions. The study results show that the oscillator is conservative and has no dissipation. It also has various dynamics,

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21

Riaz, Muhammad Bilal, Adil Jhangeer, Jan Martinovic, and Syeda Sarwat Kazmi. "Dynamics and Soliton Propagation in a Modified Oskolkov Equation: Phase Plot Insights." Symmetry 15, no. 12 (2023): 2171. http://dx.doi.org/10.3390/sym15122171.

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This study explores the modified Oskolkov equation, which depicts the behavior of the incompressible viscoelastic Kelvin–Voigt fluid. The primary focus of this research lies in several key areas. Firstly, the Lie symmetries of the considered equation are identified. These symmetries are utilized to transform the discussed model into an ordinary differential equation. Analytical solutions are subsequently derived using the new auxiliary equation technique. Next, a comprehensive analysis of the equation’s dynamic nature is undertaken from multiple aspects. Bifurcation is carried out at fixed poi

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Abdulkerim, Sohayb, Athanasios Dafnis, and Hans-G. Riemerdes. "Experimental Investigation of Nonlinear Vibration of a Thin Rectangular Plate." International Journal of Applied Mechanics 11, no. 06 (2019): 1950059. http://dx.doi.org/10.1142/s1758825119500595.

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In this paper, the geometrical nonlinear vibrations of a rectangular plate have been investigated experimentally and numerically. The experiment was conducted on a thin rectangular plate. The plate was excited close to the first fundamental natural frequency. The time history of velocities of the central point has been measured by using a laser vibrometer. While the numerical investigation has been carried using the Finite Element Method (FEM), the numerical results are validated by analytical and experimental results. In order to develop and test the extraction procedure of the bifurcation pl

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Rahim, Muhammad Firdaus Abdul, Hayder Natiq, and Nur Aisyah Abdul Fataf. "Studying the Dynamics and Complexity of a 3D Laser Plasma System." Solid State Phenomena 317 (May 2021): 556–63. http://dx.doi.org/10.4028/www.scientific.net/ssp.317.556.

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In this paper, a 3D laser plasma interaction system is presented, analysed, and implemented. The system has two unstable equilibria, and two types of coexisting attractors in which the coexistence of two periodic orbits and the coexistence of two chaotic attractors can be clearly observed. The multistability behaviours are determined by the bifurcation diagrams, largest Lyapunov exponents, and phase spaces. Moreover, the complexity performance of the laser plasma interaction system is investigated by the contour plot of the Sample Entropy.

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Tang, Qiansheng, Chaofeng Li, and Bangchun Wen. "Analysis on Forced Vibration of Thin-Wall Cylindrical Shell with Nonlinear Boundary Condition." Shock and Vibration 2016 (2016): 1–22. http://dx.doi.org/10.1155/2016/8978932.

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Forced vibration of thin-wall cylindrical shell under nonlinear boundary condition was discussed in this paper. The nonlinear boundary was modeled as supported clearance in one end of shell and the restraint was assumed as linearly elastic in the radial direction. Based on Sanders’ shell theory, Lagrange equation was utilized to derive the nonlinear governing equations of cylindrical shell. The displacements in three directions were represented by beam functions and trigonometric functions. In the study of nonlinear dynamic responses of thin-wall cylindrical shell with supported clearance unde

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Badsiwal, Renu, Sudesh Kumari, and Renu Chugh. "Dynamical behavior of q-deformed logistic map in superior orbit." Studia Universitatis Babes-Bolyai Matematica 69, no. 1 (2024): 149–70. http://dx.doi.org/10.24193/subbmath.2024.1.10.

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In this paper, we study the q-deformed logistic map in Mann orbit (superior orbit) which is a two-step fixed-point iterative algorithm. The main aim of this paper is to investigate the whole dynamical behavior of the proposed map through various techniques such as fixed-point and stability approach, time-series analysis, bifurcation plot, Lyapunov exponent and cobweb diagram. We notice that the chaotic behavior of q-deformed logistic map can be controlled by choosing control parameters carefully. The convergence and stability range of the map can be increased substantially. Moreover, with the

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Mukhopadhyay, Debkusum, and Samares Pal. "Efficacy of Isolation as a Control Strategy for Ebola Outbreaks in Combination with Vaccination." Biophysical Reviews and Letters 14, no. 03 (2019): 115–39. http://dx.doi.org/10.1142/s179304801950005x.

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In this research work, we have developed and analyzed a deterministic epidemiological model with a system of nonlinear differential equations for controlling the spread of Ebola virus disease (EVD) in a population with vital dynamics (where birth and death rates are not equal). The model examines the disease transmission dynamics with isolation from exposed and infected human class and effect of vaccination in susceptible human population through stability analysis and bifurcation analysis. The model exhibits two steady state equilibria, namely, disease-free and endemic equilibrium. Next gener

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Samuelson, Meg. "Literature in the World: A View from Cape Town." PMLA/Publications of the Modern Language Association of America 131, no. 5 (2016): 1544–47. http://dx.doi.org/10.1632/pmla.2016.131.5.1544.

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Returning Recently to Teach at My Alma Mater, The University of Cape Town, I Was Amazed to Find That the Undergraduate curriculum to which I had been exposed at the dawn of the post-apartheid era remained substantially unaltered. With the exception of an experimentally convened introductory year that reverses chronology with interesting effects, the English major continues to plot a literary history across four inherited periods: Shakespeare and Co., Romance to Realism, Modernism, and Contemporary Literature, which collapses a previous bifurcation of the capstone course into Postmodernism or P

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Longsuo, Li. "Suppressing Chaos of Duffing-Holmes System Using Random Phase." Mathematical Problems in Engineering 2011 (2011): 1–8. http://dx.doi.org/10.1155/2011/538202.

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The effect of random phase for Duffing-Holmes equation is investigated. We show that as the intensity of random noise properly increases the chaotic dynamical behavior will be suppressed by the criterion of top Lyapunov exponent, which is computed based on the Khasminskii's formulation and the extension of Wedig's algorithm for linear stochastic systems. Then, the obtained results are further verified by the Poincaré map analysis, phase plot, and time evolution on dynamical behavior of the system, such as stability, bifurcation, and chaos. Thus excellent agrement between these results is found

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Atobe, Takashi. "Lagrangian Chaos in the Stokes Flow Between Two Eccentric Rotating Cylinders." International Journal of Bifurcation and Chaos 07, no. 05 (1997): 1007–23. http://dx.doi.org/10.1142/s0218127497000820.

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Chaotic motion of the fluid particles in the Stokes flow between two eccentric cylinders rotating alternately is investigated numerically, analytically and experimentally. We examine the dependence of the motion of the fluid particles on the eccentricity ε, focusing on an equilibrium point of the Poincaré plot. When the bifurcation of the equilibrium point from the elliptic to the hyperbolic type occurs at ε = εb, the area of the chaotic region takes a maximum around εb. The results from the perturbation analysis show good agreement with the numerical results. The orbital instability of the mo

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Karoun, Rabia Chaimaà, Adel Ouannas, Mohammed Al Horani, and Giuseppe Grassi. "The Effect of Caputo Fractional Variable Difference Operator on a Discrete-Time Hopfield Neural Network with Non-Commensurate Order." Fractal and Fractional 6, no. 10 (2022): 575. http://dx.doi.org/10.3390/fractalfract6100575.

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In this work, we recall some definitions on fractional calculus with discrete-time. Then, we introduce a discrete-time Hopfield neural network (D.T.H.N.N) with non-commensurate fractional variable-order (V.O) for three neurons. After that, phase-plot portraits, bifurcation and Lyapunov exponents diagrams are employed to verify that the proposed discrete time Hopfield neural network with non-commensurate fractional variable order has chaotic behavior. Furthermore, we use the 0-1 test and C0 complexity algorithm to confirm and prove the results obtained about the presence of chaos. Finally, simu

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Kang, Jaeyoung. "Nonlinear Vibration Induced by Friction in a Ball Joint System." Lubricants 10, no. 9 (2022): 201. http://dx.doi.org/10.3390/lubricants10090201.

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In this paper, the nonlinear oscillations induced by friction in a ball-on-socket system are investigated. The nonlinear time response was obtained by solving the differential equations of the friction-noise model of the finite element ball with multiple modes. The different patterns of motion were analyzed via the bifurcation diagram, Poincare map, and recurrence plot. The Lyapunov exponents of the discontinuous system with distributed contact were calculated using the Muller method. From the analysis, it is shown that a friction-noise of a ball joint can retain periodic, quasi-periodic, or c

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Rajagopal, Karthikeyan, Fahimeh Nazarimehr, Anitha Karthikeyan, Ashokkumar Srinivasan, and Sajad Jafari. "CAMO: Self-Excited and Hidden Chaotic Flows." International Journal of Bifurcation and Chaos 29, no. 11 (2019): 1950143. http://dx.doi.org/10.1142/s0218127419501438.

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In this paper, we announce a novel 4D chaotic system which belongs to the self-excited attractor and hidden attractor family depending on the parameter values. Lyapunov exponents, bifurcation diagram and bicoherence plot of the CAMO (Camouflage) chaotic system are investigated. Also, fractional-order model of the proposed CAMO system (FOCAMO) is derived and analyzed. FOCAMO chaotic system is then implemented in Field Programmable Gate Array (FPGA) using Adomian decomposition method. Also, power efficiency analysis for various fractional-orders is investigated. The paper helps build a better un

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Rui, Weiguo. "Exact Traveling Wave Solutions for a Nonlinear Evolution Equation of Generalized Tzitzéica-Dodd-Bullough-Mikhailov Type." Journal of Applied Mathematics 2013 (2013): 1–14. http://dx.doi.org/10.1155/2013/395628.

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By using the integral bifurcation method, a generalized Tzitzéica-Dodd-Bullough-Mikhailov (TDBM) equation is studied. Under different parameters, we investigated different kinds of exact traveling wave solutions of this generalized TDBM equation. Many singular traveling wave solutions with blow-up form and broken form, such as periodic blow-up wave solutions, solitary wave solutions of blow-up form, broken solitary wave solutions, broken kink wave solutions, and some unboundary wave solutions, are obtained. In order to visually show dynamical behaviors of these exact solutions, we plot graphs

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Lawnik, Marcin, and Marek Berezowski. "New Chaotic System: M-Map and Its Application in Chaos-Based Cryptography." Symmetry 14, no. 5 (2022): 895. http://dx.doi.org/10.3390/sym14050895.

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One of the applications of dynamical systems with chaotic behavior is data encryption. Chaos-based cryptography uses chaotic dynamical systems as the basis for creating algorithms. The present article discusses a new dynamical system called M-map with its analysis: fixed points, bifurcation diagram, Lyapunov exponent, and invariant density. The obtained bifurcation diagram and the plot of the Lyapunov exponent (with a minimum value of ln2 and a maximum value of ln4) suggest that the so-called robust chaos characterizes this map. Moreover, the obtained results are compared with other dynamical

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PREMALATHA, L., and P. VANAJARANJAN. "USE OF RECURRENCE PLOT ANALYSIS FOR DETECTING CHAOS AND NOISE IN NONLINEAR SWITCHING CIRCUITS." Journal of Circuits, Systems and Computers 15, no. 03 (2006): 409–36. http://dx.doi.org/10.1142/s0218126606003209.

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DC–DC converters controlled by naturally sampled, constant frequency pulse width modulation give rise to a wide range of bifurcation and chaos depending on the change in the system parameter values. Knowledge of transitions from regular to chaotic behavior is essential to understand the underlying dynamics of nonlinear switching circuits. While linear approaches are often insufficient to describe such processes, there are nonlinear methods available but requires long time observations. To overcome these difficulties, a newly developed pattern recognition method of nonlinear dynamics called Rec

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Danca, Marius-F., and Nikolay Kuznetsov. "Hidden Strange Nonchaotic Attractors." Mathematics 9, no. 6 (2021): 652. http://dx.doi.org/10.3390/math9060652.

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In this paper, it is found numerically that the previously found hidden chaotic attractors of the Rabinovich–Fabrikant system actually present the characteristics of strange nonchaotic attractors. For a range of the bifurcation parameter, the hidden attractor is manifestly fractal with aperiodic dynamics, and even the finite-time largest Lyapunov exponent, a measure of trajectory separation with nearby initial conditions, is negative. To verify these characteristics numerically, the finite-time Lyapunov exponents, ‘0-1’ test, power spectra density, and recurrence plot are used. Beside the cons

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Rui, Weiguo. "Exact Solutions of a High-Order Nonlinear Wave Equation of Korteweg-de Vries Type under Newly Solvable Conditions." Abstract and Applied Analysis 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/714214.

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By using the integral bifurcation method together with factoring technique, we study a water wave model, a high-order nonlinear wave equation of KdV type under some newly solvable conditions. Based on our previous research works, some exact traveling wave solutions such as broken-soliton solutions, periodic wave solutions of blow-up type, smooth solitary wave solutions, and nonsmooth peakon solutions within more extensive parameter ranges are obtained. In particular, a series of smooth solitary wave solutions and nonsmooth peakon solutions are obtained. In order to show the properties of these

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Sudesh, Kumari, Chugh Renu, and Nandal Ashish. "Controlling the Chaos of Logistic Map using Switching Strategy." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 2 (2019): 515–18. https://doi.org/10.35940/ijeat.B2987.129219.

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In our very recent work (2019), we extended the stability performance of logistic map up to a higher value of r using SP orbit. In this article, we further extend this range of stability by adopting switching strategy (Parrondo’s Paradox) of controlling the chaos of dynamical systems. We observe that even the earlier chaotic orbits of four step feedback procedure can be converted into periodic orbits. Our approach can be used to solve a wider circle of engineering problems.

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KATSANIKAS, M., P. A. PATSIS, and G. CONTOPOULOS. "THE STRUCTURE AND EVOLUTION OF CONFINED TORI NEAR A HAMILTONIAN HOPF BIFURCATION." International Journal of Bifurcation and Chaos 21, no. 08 (2011): 2321–30. http://dx.doi.org/10.1142/s0218127411029811.

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We study the orbital behavior at the neighborhood of complex unstable periodic orbits in a 3D autonomous Hamiltonian system of galactic type. At a transition of a family of periodic orbits from stability to complex instability (also known as Hamiltonian Hopf Bifurcation) the four eigenvalues of the stable periodic orbits move out of the unit circle. Then the periodic orbits become complex unstable. In this paper, we first integrate initial conditions close to the ones of a complex unstable periodic orbit, which is close to the transition point. Then, we plot the consequents of the correspondin

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Huang, Yimin, and Qiuxiang Li. "The Entropy Complexity of an Asymmetric Dual-Channel Supply Chain with Probabilistic Selling." Entropy 20, no. 7 (2018): 543. http://dx.doi.org/10.3390/e20070543.

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Considering consumers’ attitudes to risks for probabilistic products and probabilistic selling, this paper develops a dynamic Stackelberg game model of the supply chain considering the asymmetric dual-channel structure. Based on entropy theory and dynamic theory, we analyze and simulate the influences of decision variables and parameters on the stability and entropy of asymmetric dual-channel supply chain systems using bifurcation, entropy diagram, the parameter plot basin, attractor, etc. The results show that decision variables and parameters have great impacts on the stability of asymmetric

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Korolyova, Vera V. "Myth about Leonardo the artist in the novels "Resurrection of Gods. Leonardo da Vinci" by Dmitry Merezhkovsky and "The Devil's Elixirs" by E. T. A. Hoffmann." Vestnik of Kostroma State University, no. 2 (2019): 159–64. http://dx.doi.org/10.34216/1998-0817-2019-25-2-159-164.

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The novel "The Devil's Elixirs" by E. T. A. Hoffmann is considered in this article as one of possible references of the myth about Leonardo in the work "Resurrection of Gods. Leonardo da Vinci" by Dmitry Merezhkovsky. This statement is based on comparative identification of community of plot, perspective and images. Opposition of Christianity and Paganisms (apostasy), Man and art (genuine art vs. fake one), society mechanisation problem, human consciousness bifurcation and search of spiritual synthesis are central in the novels by E. T. A. Hoffman and Dmitry Merezhkovsky. A number of E. T. A.

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Sahoo, Bamadev, L. N. Panda, and Goutam Pohit. "Nonlinear Dynamics of a Travelling Beam Subjected to Multi-Frequency Parametric Excitation." Applied Mechanics and Materials 592-594 (July 2014): 2076–80. http://dx.doi.org/10.4028/www.scientific.net/amm.592-594.2076.

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This paper deals with two frequency parametric excitation in presence of internal resonance. The cubic nonlinearity is inserted into the equation of motion by considering the mid-line stretching of the beam. The perturbation method of multiple scales is applied directly to the governing nonlinear fourth order integro-partial differential equation of motion. This leads to a set of first order differential equations known as the reduced equations or normalized reduced equations, which are utilized to determine the additional instability zones, appeared in the trivial state stability plot, the bi

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Jana, Debaldev. "Stabilizing Effect of Prey Refuge and Predator’s Interference on the Dynamics of Prey with Delayed Growth and Generalist Predator with Delayed Gestation." International Journal of Ecology 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/429086.

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In the present paper, I study a prey-predator model with multiple time delays where the predator population is regarded as generalist. For this regard, I consider a Holling-Tanner prey-predator system where a constant time delay is incorporated in the logistic growth of the prey to represent a delayed density dependent feedback mechanism and the second time delay is considered to account for the length of the gestation period of the predator. Predator’s interference in predator-prey relationship provides better descriptions of predator's feeding over a range of prey-predator abundances, so the

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Xia, Yan, Yi Wan, Hongwei Wang, and Zhanqiang Liu. "Dynamic characteristics analysis of locomotive traction gear pair system under internal and external excitations." Engineering Computations 37, no. 8 (2020): 2587–617. http://dx.doi.org/10.1108/ec-03-2019-0083.

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Purpose As the transmission component of a locomotive, the traction gear pair system has a direct effect on the stability and reliability of the whole machine. This paper aims to provide a detailed dynamic analysis for the traction system under internal and external excitations by numerical simulation. Design/methodology/approach A non-linear dynamic model of locomotive traction gear pair system is proposed, where the comprehensive time-varying meshing stiffness is obtained through the Ishikawa formula method and verified by the energy method, and then the sliding friction excitation is analyz

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Gaspar, José M. "Bridging the Gap between Economic Modelling and Simulation: A Simple Dynamic Aggregate Demand-Aggregate Supply Model with Matlab." Journal of Applied Mathematics 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/3193068.

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This paper aims to connect the bridge between analytical results and the use of the computer for numerical simulations in economics. We address the analytical properties of a simple dynamic aggregate demand and aggregate supply (AD-AS) model and solve it numerically. The model undergoes a bifurcation as its steady state smoothly interchanges stability depending on the relationship between the impact of real interest rate on demand for liquidity and how fast agents revise their expectations on inflation. Using code embedded into a unique function in Matlab, we plot the numerical solutions of th

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Yi-min, Huang, Li Qiu-xiang, and Zhang Yu-hao. "The Complexity Analysis for Price Game Model of Risk-Averse Supply Chain Considering Fairness Concern." Complexity 2018 (December 2, 2018): 1–15. http://dx.doi.org/10.1155/2018/9216193.

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This paper, considering risk aversion and fair concern, establishes a dynamic price game model of a dual-channel supply chain in which dual-channel retailer sells products through traditional channel and online channel and the online retailer only sells products through online channel. The stability of the system and the influences of different parameter values on utilities are analyzed emphatically using game theory and nonlinear dynamic theory, such as 2D and 3D bifurcation diagram, parameter plot basin, chaos attractor, and sensitivity to initial value. The results find that the system is m

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Danca, Marius-F. "Matlab Code for Lyapunov Exponents of Fractional-Order Systems, Part II: The Noncommensurate Case." International Journal of Bifurcation and Chaos 31, no. 12 (2021): 2150187. http://dx.doi.org/10.1142/s021812742150187x.

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In this paper, the Benettin–Wolf algorithm for determining all Lyapunov exponents of noncommensurate fractional-order systems modeled by Caputo’s derivative and the corresponding Matlab code are presented. The paper continues the work started in [ Danca & Kuznetsov, 2018 ], where the Matlab code of commensurate fractional-order systems is given. To integrate the extended systems, the Adams–Bashforth–Moulton scheme for fractional differential equations is utilized. Like the Matlab program for commensurate-order systems, the program presented in this paper prints and plots all Lyapunov expon

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Cheng, Zhiqiang, Wencheng Wang, Yuezhang Dai, and Lun Li. "Novel One-Dimensional Chaotic System and Its Application in Image Encryption." Complexity 2022 (October 18, 2022): 1–16. http://dx.doi.org/10.1155/2022/1720842.

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Designing a chaotic system with a simple structure and complex dynamic behavior is one of the main tasks of chaotic cryptography. This paper designs a new 1D chaotic system called 1D two-parameters-sin-cos (1D-TPSC). Compared with high-dimensional chaotic systems, the 1D-TPSC has a simple structure and is easy to implement with software. The Lyapunov exponent analyzes the parameter space of the 1D-TPSC in a chaotic state. Furthermore, using sensitivity analysis, cobweb plot, and bifurcation diagram to verify that the sequence generated by 1D-TPSC has good performance. In addition, the 1D-TPSC

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Elmandouh, Adel, Aqilah Aljuaidan, and Mamdouh Elbrolosy. "The Integrability and Modification to an Auxiliary Function Method for Solving the Strain Wave Equation of a Flexible Rod with a Finite Deformation." Mathematics 12, no. 3 (2024): 383. http://dx.doi.org/10.3390/math12030383.

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Our study focuses on the governing equation of a finitely deformed flexible rod with strain waves. By utilizing the well-known Ablowita–Ramani–Segur (ARS) algorithm, we prove that the equation is non-integrable in the Painlevé sense. Based on the bifurcation theory for planar dynamical systems, we modify an auxiliary equation method to obtain a new systematic and effective method that can be used for a wide class of non-linear evolution equations. This method is summed up in an algorithm that explains and clarifies the ease of its applicability. The proposed method is successfully applied to c

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Anistratenko, Antonina V. "ALTERNATIVE HISTORY GENRE IN THE FINE LITERATURE. THE ROLE OF EUROPEAN MYTH IN CRYPTOHISTORICAL WRITING." Alfred Nobel University Journal of Philology 2, no. 24 (2022): 8–16. http://dx.doi.org/10.32342/2523-4463-2022-2-24-1.

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The article is devoted to the Alternative History (AH) genre in fiction and function of the “European Myth” in cryptohistorical writing. The article aims to determine the identity and path of the alternative historical novel in Ukraine and its comparative characteristics at the current stage of modern fiction. The tasks of the study are to determine the ways of European myth functioning in the artistic space of the neomodern AI novel in Ukraine which creates a new genealogical pattern in Ukrainian literary studies. Research methods are subordinate to the aim of the study and tasks. They are co

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