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Journal articles on the topic 'Auxiliary modulating dynamical systems'

Author: Grafiati

Published: 7 July 2024

Last updated: 31 July 2025

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1

Liu, Jie, Da-Yan Liu, Driss Boutat, Xuefeng Zhang, and Ze-Hao Wu. "Innovative non-asymptotic and robust estimation method using auxiliary modulating dynamical systems." Automatica 152 (June 2023): 110953. http://dx.doi.org/10.1016/j.automatica.2023.110953.

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2

Stark, Oliver, Marius Eckert, Albertus Johannes Malan, and Sören Hohmann. "Fractional Systems’ Identification Based on Implicit Modulating Functions." Mathematics 10, no. 21 (2022): 4106. http://dx.doi.org/10.3390/math10214106.

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This paper presents a new method for parameter identification based on the modulating function method for commensurable fractional-order models. The novelty of the method lies in the automatic determination of a specific modulating function by controlling a model-based auxiliary system, instead of applying and parameterizing a generic modulating function. The input signal of the model-based auxiliary system used to determine the modulating function is designed such that a separate identification of each individual parameter of the fractional-order model is enabled. This eliminates the shortcom

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3

Catanach, Thomas A., and James L. Beck. "Bayesian System Identification using auxiliary stochastic dynamical systems." International Journal of Non-Linear Mechanics 94 (September 2017): 72–83. http://dx.doi.org/10.1016/j.ijnonlinmec.2017.03.012.

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4

Grechko, D. A., N. V. Barabash, and V. N. Belykh. "Homoclinic Orbits and Chaos in Nonlinear Dynamical Systems: Auxiliary Systems Method." Lobachevskii Journal of Mathematics 42, no. 14 (2021): 3365–71. http://dx.doi.org/10.1134/s199508022202007x.

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5

Sheng, Yicheng, Sihan Xu, Caishi Zhang, Binghua Su, Dingxiang Cao, and Zhe Chen. "Zoom Auxiliary Imaging Lens Design for a Modulation Transfer Function Test System." Photonics 12, no. 1 (2025): 53. https://doi.org/10.3390/photonics12010053.

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In this paper, we propose a zoom auxiliary imaging lens based on the four-component mechanical zoom method for a modulation transfer function (MTF) test system. The auxiliary imaging lenses of the current MTF test system typically use fixed-focus optical systems, which are unable to meet the test scenarios of fast and batch measurement and measure lenses with an extensive focal length range. Compared with the fixed-focus auxiliary imaging lens, the zoom auxiliary imaging lens can simultaneously satisfy the measurement of wide-angle and telephoto miniature lenses without losing measurement accu

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6

El Allaoui, Abdelati, Said Melliani, and Lalla Saadia Chadli. "Stability of Fuzzy Dynamical Systems via Lyapunov Functions." International Journal of Differential Equations 2020 (August 1, 2020): 1–7. http://dx.doi.org/10.1155/2020/6218424.

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The purpose of this paper is to introduce the concept of fuzzy Lyapunov functions to study the notion of stability of equilibrium points for fuzzy dynamical systems associated with fuzzy initial value problems, through the principle of Zadeh. Our contribution consists in a qualitative characterization of stability by a study of the trajectories of fuzzy dynamical systems, using auxiliary functions, and they will be called fuzzy Lyapunov functions. And, among the main results that have been proven is that the existence of fuzzy Lyapunov functions is a necessary and sufficient condition for stab

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7

Fang-Hong, Xiao, Yan Gui-Rong, and Zhang Xin-Wu. "Effect of signal modulating noise in bistable stochastic dynamical systems." Chinese Physics 12, no. 9 (2003): 946–50. http://dx.doi.org/10.1088/1009-1963/12/9/304.

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8

ZHANG, YONGXIANG. "CHARACTERIZING FRACTAL BASIN BOUNDARIES FOR PLANAR SWITCHED SYSTEMS." Fractals 25, no. 03 (2017): 1750031. http://dx.doi.org/10.1142/s0218348x17500311.

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This paper is to introduce some analytical tools to characterize the properties of fractal basin boundaries for planar switched systems (with time-dependent switching). The characterizing methods are based on the view point of limit sets and prime ends. By constructing the auxiliary dynamical system, the fractal basin boundaries of planar switched systems can be proved if every diverging path in the basin of associated auxiliary system has the entire basin boundary as its limit set. Fractal property is also verified if every prime end that is defined in the basin of associated auxiliary system

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Kopysov, Oleg. "Identification of Physical Dynamical Processes Via Linear Structure Models (Part 2)." International Journal of Systems Engineering 8, no. 2 (2024): 22–39. http://dx.doi.org/10.11648/j.ijse.20240802.11.

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Well-known methods of joint estimation of the state and parameters (quasilinearization, invariant imbedding, extended Kalman filter and others like them) expand the vector of the state of the system by including equations for parameters in the model. Such a task of joint estimation of the state and parameter is nonlinear even for linear systems. For Linear Structure Models (LSModels), an analytical method is proposed for the transition to an auxiliary model in which the parameter vector is expanded by initial states and the task of identifying parameter and initial states becomes linear. With

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10

Tang, Jia-Liang, Gabriel Alvarado Barrios, Enrique Solano, and Francisco Albarrán-Arriagada. "Tunable Non-Markovianity for Bosonic Quantum Memristors." Entropy 25, no. 5 (2023): 756. http://dx.doi.org/10.3390/e25050756.

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We studied the tunable control of the non-Markovianity of a bosonic mode due to its coupling to a set of auxiliary qubits, both embedded in a thermal reservoir. Specifically, we considered a single cavity mode coupled to auxiliary qubits described by the Tavis–Cummings model. As a figure of merit, we define the dynamical non-Markovianity as the tendency of a system to return to its initial state, instead of evolving monotonically to its steady state. We studied how this dynamical non-Markovianity can be manipulated in terms of the qubit frequency. We found that the control of the auxiliary sys

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11

Sabi’u, Jamilu, Mustafa Inc, Temesgen Leta, Dumitru Baleanu, and Hadi Rezazadeh. "Dynamical behaviour of the Joseph-Egri equation." Thermal Science 27, Spec. issue 1 (2023): 19–28. http://dx.doi.org/10.2298/tsci23s1019s.

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We investigate traveling wave solutions to the Joseph-Egri equation via extended auxiliary equation technique. We have determined stationary points of the dynamical systems by using bifurcation method. We also acquire cusp, periodic and homoclinic orbits. The investigated solutions are entirely different from the reported in the liter?ature. However, some of the reported solutions are plotted to understand the physical application of the considered model using renowned mathematical software.

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12

Abe, Sumiyoshi. "Weak invariants in dissipative systems: action principle and Noether charge for kinetic theory." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2170 (2020): 20190196. http://dx.doi.org/10.1098/rsta.2019.0196.

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In non-equilibrium classical thermostatistics, the state of a system may be described by not only dynamical/thermodynamical variables but also a kinetic distribution function. This ‘double structure’ bears some analogy with that in quantum thermodynamics, where both dynamical variables and the Hilbert space are involved. Recently, the concept of weak invariants has repeatedly been discussed in the context of quantum thermodynamics. A weak invariant is defined in such a way that its value changes in time but its expectation value is conserved under time evolution prescribed by a kinetic equatio

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13

Ene, Remus-Daniel, Nicolina Pop, and Rodica Badarau. "Symmetries and Closed-Form Solutions for Some Classes of Dynamical Systems." Symmetry 17, no. 4 (2025): 546. https://doi.org/10.3390/sym17040546.

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The present paper focuses on some classes of dynamical systems involving Hamilton–Poisson structures, while neglecting their chaotic behaviors. Based on this, the closed-form solutions are obtained. These solutions are derived using the Optimal Auxiliary Functions Method (OAFM). The impact of the physical parameters of the system is also investigated. Periodic orbits around the equilibrium points are performed. There are homoclinic or heteroclinic orbits and they are obtained in exact form. The dynamical system is reduced to a second-order nonlinear differential equation, which is analytically

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14

Chaturvedi, Siddharth, Ahmed El-Gazzar, and Marcel van Gerven. "A dynamical systems approach to optimal foraging." PLOS Complex Systems 1, no. 3 (2024): e0000018. http://dx.doi.org/10.1371/journal.pcsy.0000018.

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Foraging for resources in an environment is a fundamental activity that must be addressed by any biological agent. Modelling this phenomenon in simulations can enhance our understanding of the characteristics of natural intelligence. In this work, we present a novel approach to model foraging in-silico using a continuous coupled dynamical system. The dynamical system is composed of three differential equations, representing the position of the agent, the agent’s control policy, and the environmental resource dynamics. Crucially, the control policy is implemented as a parameterized differential

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15

Pumaricra Rojas, David, Matti Noack, Johann Reger, and Gustavo Pérez-Zúñiga. "State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions." Sensors 22, no. 13 (2022): 5008. http://dx.doi.org/10.3390/s22135008.

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Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary sy

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16

David, Pumaricra Rojas, Noack Matti, Reger Johann, and Pérez-Zúñiga Gustavo. "State Estimation for Coupled Reaction-Diffusion PDE Systems Using Modulating Functions." Sensors 2022 22, no. 13 (2022): 5008. https://doi.org/10.3390/s22135008.

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Many systems with distributed dynamics are described by partial differential equations (PDEs). Coupled reaction-diffusion equations are a particular type of these systems. The measurement of the state over the entire spatial domain is usually required for their control. However, it is often impossible to obtain full state information with physical sensors only. For this problem, observers are developed to estimate the state based on boundary measurements. The method presented applies the so-called modulating function method, relying on an orthonormal function basis representation. Auxiliary sy

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17

Belinskiy, Boris P., and Peter Caithamer. "Stability of Dynamical Systems with a Multiplicative White Noise." Stochastics and Dynamics 03, no. 02 (2003): 187–212. http://dx.doi.org/10.1142/s021949370300070x.

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We discuss the behavior, for large values of time, of a class of linear mechanical systems with a white noise in their parameters. The initial conditions may be random as well but are independent of white noise. It is well known that a deterministic linear mechanical system with viscous damping is stable, i.e. its energy approaches zero as time increases. We calculate the expected energy and check that this behavior takes place in the case when the initial conditions are random but the parameters are not. When the parameters contain a random noise the expected energy may be infinite, approach

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18

Zheng, Hongpeng, Yulong Lei, and Pengxiang Song. "Designing the main controller of auxiliary braking systems for heavy-duty vehicles in nonemergency braking conditions." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 232, no. 9 (2017): 1605–15. http://dx.doi.org/10.1177/0954406217706386.

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With the development of the road industry, heavy-duty vehicles now require additional braking power to fulfill their braking requirements. Auxiliary braking systems, which include a hydraulic retarder and an engine brake, can provide additional braking force in nonemergency braking conditions. A water medium retarder is a new type of hydraulic retarder that can convert the kinetic energy of a vehicle into the thermal energy of coolant. This study introduces a novel auxiliary braking system involving a water medium retarder and an engine brake for heavy-duty vehicles. The specific forces of hea

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19

MICHALSKI, Jacek. "Comparison of Auxiliary and Likelihood Particle Filters for State Estimation of Dynamical Systems." PRZEGLĄD ELEKTROTECHNICZNY 1, no. 12 (2018): 88–92. http://dx.doi.org/10.15199/48.2018.12.19.

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20

YAN, FANG, CUNCAI HUA, HAIHONG LIU, and ZENGRONG LIU. "THE EXACT TRAVELING WAVE SOLUTIONS AND THEIR BIFURCATIONS IN THE GARDNER AND GARDNER–KP EQUATIONS." International Journal of Bifurcation and Chaos 22, no. 05 (2012): 1250126. http://dx.doi.org/10.1142/s021812741250126x.

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By using the method of dynamical systems, this paper studies the exact traveling wave solutions and their bifurcations in the Gardner equation. Exact parametric representations of all wave solutions as well as the explicit analytic solutions are given. Moreover, several series of exact traveling wave solutions of the Gardner–KP equation are obtained via an auxiliary function method.

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21

Москаленко, О. И., Е. В. Евстифеев та А. А. Короновский. "Метод определения характеристик перемежающейся обобщенной синхронизации на основе расчета локальных показателей Ляпунова". Письма в журнал технической физики 46, № 16 (2020): 12. http://dx.doi.org/10.21883/pjtf.2020.16.49846.18359.

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Method for the laminar and turbulent phase detection in coupled dynamical systems being near the boundary of the generalized synchronization regime based on the calculation of local Lyapunov exponents has been proposed. The efficiency of the method has been testified using the systems with unidirectional coupling allowing the analysis of intermittency by the auxiliary system approach. The results of both methods have been compared with each other, a good agreement between them has been obtained.

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22

GOMOYUNOV, MIKHAIL, DMITRI KORNEV, and NIKOLAI LUKOYANOV. "GAME THEORY APPLICATIONS TO GUARANTEE OPTIMIZATION IN DYNAMICAL SYSTEMS WITH CONTROL DELAYS." International Game Theory Review 16, no. 02 (2014): 1440010. http://dx.doi.org/10.1142/s0219198914400106.

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In this paper, a linear dynamical system controlled under the conditions of disturbances and with control delays is considered. The Euclidean norm of a set of the system motion deviations at given instants of time from given targets is minimized. Within the game-theoretical approach the problem of calculating the value of the optimal guaranteed result and constructing a positional (closed-loop) control law that ensures this result is posed. For this problem, a solution procedure based on the recurrent construction of upper convex hulls of auxiliary program functions is elaborated. Results of n

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23

WU, ZHAOYAN, XINCHU FU, and GUANRONG CHEN. "MONITORING THE TOPOLOGY OF GROWING DYNAMICAL NETWORKS." International Journal of Modern Physics C 21, no. 08 (2010): 1051–63. http://dx.doi.org/10.1142/s012918311001566x.

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In this paper, topology monitoring of growing networks is studied. When some new nodes are added into a network, the topology of the network is changed, which needs to be monitored in many applications. Some auxiliary systems (network monitors) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied to designing such network monitors. Based on the Lyapunov function method via constructing a potential or energy function decreasing along any solution of the system, and the LaSalle's invariance principle, which is a generalization of the Lyapunov function

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24

Tokmak, Fen, Mehmet Fen, and Marat Akhmet. "A novel criterion for unpredictable motions." Filomat 37, no. 18 (2023): 6151–60. http://dx.doi.org/10.2298/fil2318151t.

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We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient conditions for the existence of unpredictable motions in the dynamics of the response system are provided. The theoretical results are exemplified for coupled autonomous systems in which the drive is a hybrid dynamical system and the response is a Lorenz system. The auxiliary system approach and conditional Lyapunov exponents are utilized to detect the presence of generalized synchronization.

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25

Azhmyakov, Vadim, and Ruben Velazquez. "On a Variational Approach to Optimization of Hybrid Mechanical Systems." Mathematical Problems in Engineering 2010 (2010): 1–13. http://dx.doi.org/10.1155/2010/978736.

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This paper deals with multiobjective optimization techniques for a class of hybrid optimal control problems in mechanical systems. We deal with general nonlinear hybrid control systems described by boundary-value problems associated with hybrid-type Euler-Lagrange or Hamilton equations. The variational structure of the corresponding solutions makes it possible to reduce the original “mechanical” problem to an auxiliary multiobjective programming reformulation. This approach motivates possible applications of theoretical and computational results from multiobjective optimization related to the

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26

Dykman, M. I., V. N. Smelyanskiy, D. G. Luchinsky, R. Mannella, P. V. E. McClintock, and N. D. Stein. "Large Fluctuations in a Periodically Driven Dynamical System." International Journal of Bifurcation and Chaos 08, no. 04 (1998): 747–54. http://dx.doi.org/10.1142/s0218127498000541.

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Fluctuations in a periodically driven overdamped oscillator are studied theoretically and experimentally in the limit of low noise intensity by investigation of their prehistory. It is shown that, for small noise intensity, fluctuations to points in coordinate space that are remote from the stable states occur along paths that form narrow tubes. The tubes are centered on the optimal paths corresponding to trajectories of an auxiliary Hamiltonian system. The optimal paths themselves, and the tubes of paths around them, are visualized through measurements of the prehistory probability distributi

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27

MANAVELLA, EDMUNDO C. "FADDEEV–JACKIW FORMALISM FOR CONSTRAINED SYSTEMS WITH GRASSMANN DYNAMICAL FIELD VARIABLES." International Journal of Modern Physics A 27, no. 24 (2012): 1250145. http://dx.doi.org/10.1142/s0217751x1250145x.

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The Faddeev–Jackiw canonical quantization formalism for constrained systems with Grassmann dynamical variables within the framework of the field theory is reviewed. First, by means of a iterative process, the symplectic supermatrix is constructed and their associated constraints are found. Next, by taking into account the phase space of the system, the constraint structure is considered. It is found that, if there are no auxiliary dynamical field variables, the supermatrix whose elements are the Bose–Fermi brackets between the constraints associated with the independent dynamical field variabl

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28

Ene, Remus-Daniel, Nicolina Pop, and Rodica Badarau. "Exact Parametric and Semi-Analytical Solutions for the Rucklidge-Type Dynamical System." Mathematics 13, no. 13 (2025): 2052. https://doi.org/10.3390/math13132052.

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The behavior of the Rucklidge-type dynamical system was investigated, providing some semi-analytical solutions, in this paper. This system was analytically investigated by means of the Optimal Auxiliary Functions Method (OAFM) for two cases. An exact parametric solution was obtained. The effect of the physical parameters was investigated on the asymptotic behaviors and damped oscillations of the solutions. Damped oscillations are essential for analyzing and designing various mechanical, biological, and electrical systems. Many of the applications involving these systems represent the main reas

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29

AlShejari, A. A., M. A. Noor, and K. I. Noor. "Recent Developments in General Quasi Variational Inequalities." International Journal of Analysis and Applications 22 (May 20, 2024): 84. http://dx.doi.org/10.28924/2291-8639-22-2024-84.

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In this paper, we present a number of new and known numerical techniques for solving general quasi variational inequalities, introduced by Noor [34] in 1988, using various techniques including projection, Wiener-Hopf equations, auxiliary principle, dynamical systems coupled with finite difference approach and sensitivity analysis. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis is also investigated. Some special cases are discussed as applications of the main results. Several open problems are suggested for future research.

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30

Pianta, Camilla, Roberto Capuzzo-Dolcetta, and Giovanni Carraro. "The Impact of Binaries on the Dynamical Mass Estimate of Dwarf Galaxies." Astrophysical Journal 939, no. 1 (2022): 3. http://dx.doi.org/10.3847/1538-4357/ac9303.

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Abstract Binary stars are recognized to be important in driving the dynamical evolution of stellar systems and also in determining some of their observational features. In this study, we explore the role that binary stars have in modulating the estimates of the velocity dispersion of stellar systems. To this aim, we developed a tool that allows investigation of the dependence of synthetic velocity dispersion on a number of crucial quantities characterizing the binary content: binary fraction and the distributions of their mass ratio, eccentricity, and semimajor axis. As an application, we eval

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31

Parker, Jeremy P. "The Lorenz system as a gradient-like system." Nonlinearity 37, no. 9 (2024): 095022. http://dx.doi.org/10.1088/1361-6544/ad68bb.

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Abstract We formulate, for continuous-time dynamical systems, a sufficient condition to be a gradient-like system, i.e. that all bounded trajectories approach stationary points and therefore that periodic orbits, chaotic attractors, etc do not exist. This condition is based upon the existence of an auxiliary function defined over the state space of the system, in a way analogous to a Lyapunov function for the stability of an equilibrium. For polynomial systems, Lyapunov functions can be found computationally by using sum-of-squares optimisation. We demonstrate this method by finding such an au

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32

Ebrahimi, Reza, Mostafa Ghayour, and Heshmatallah Mohammad Khanlo. "Effects of some design parameters on bifurcation behavior of a magnetically supported coaxial rotor in auxiliary bearings." Engineering Computations 34, no. 7 (2017): 2379–95. http://dx.doi.org/10.1108/ec-04-2017-0141.

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Purpose This paper aims to present bifurcation analysis of a magnetically supported coaxial rotor model in auxiliary bearings, which includes gyroscopic moments of disks and geometric coupling of the magnetic actuators. Design/methodology/approach Ten nonlinear equations of motion were solved using the Runge–Kutta method. The vibration responses were analyzed using dynamic trajectories, power spectra, Poincaré maps, bifurcation diagrams and the maximum Lyapunov exponent. The analysis was carried out for different system parameters, namely, the inner shaft stiffness, inter-rotor bearing stiffne

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33

Cassal-Quiroga, B. B., and E. Campos-Cantón. "Generation of Dynamical S-Boxes for Block Ciphers via Extended Logistic Map." Mathematical Problems in Engineering 2020 (March 19, 2020): 1–12. http://dx.doi.org/10.1155/2020/2702653.

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In this work, we present a simple algorithm to design n × n-bits substitution boxes (S-boxes) based on chaotic time series of the logistic map for different carrying capacities. The use of different carrying capacities in the chaotic map leads to low computational complexity, which is desirable to get high-speed communication systems. We generate a main sequence by means of two auxiliary sequences with uniform distribution via the logistic map for different carrying capacities. The elements of the main sequence are useful for generating the elements of an S-box. The auxiliary sequences are gen

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34

Kretchmer, Joshua S., and Thomas F. Miller III. "Kinetically-constrained ring-polymer molecular dynamics for non-adiabatic chemistries involving solvent and donor–acceptor dynamical effects." Faraday Discussions 195 (2016): 191–214. http://dx.doi.org/10.1039/c6fd00143b.

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We investigate the performance of the recently developed kinetically-constrained ring polymer molecular dynamics (KC-RPMD) method for the description of model condensed-phase electron transfer (ET) reactions in which solvent and donor–acceptor dynamics play an important role. Comparison of KC-RPMD with results from Golden-Rule rate theories and numerically exact quantum dynamics calculations demonstrates that KC-RPMD accurately captures the combination of electronic- and nuclear-dynamical effects throughout the Marcus (intermediate solvent friction) and Zusman (large solvent friction) regimes

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35

Aslan, İsmail. "Traveling Waves of DDEs with Rational Nonlinearity." International Journal of Nonlinear Sciences and Numerical Simulation 17, no. 5 (2016): 243–48. http://dx.doi.org/10.1515/ijnsns-2016-0028.

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AbstractIt has been found that the dynamical behavior of many complex physical systems can be properly described by nonlinear DDEs. However, in the related literature, research focusing on such equations with rational nonlinearity is rare. Hence, the present study makes an attempt to fill the existing gap. To this end, we consider two distinct DDEs with rational nonlinearity. We observed that the model equations assume three kinds of traveling wave solutions; hyperbolic, trigonometric and rational including kink-type solitary waves and singular periodic solutions. Our discussion is based on th

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36

Liu, Lizhi, Zilin Gao, and Yi Peng. "Synchronization Mechanism for Controlled Complex Networks under Auxiliary Effect of Dynamic Edges." Electronics 13, no. 10 (2024): 1990. http://dx.doi.org/10.3390/electronics13101990.

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The scope of complex dynamical networks (CDNs) with dynamic edges is very wide, as it is composed of a class of realistic networks including web-winding systems, communication networks, neural networks, etc. However, a classic research topic in CDNs, the synchronization control problem, has not been effectively solved for CDNs with dynamic edges. This paper will investigate the emergence mechanism of synchronization from the perspective of large-scale systems. Firstly, a CDN with dynamic edges is conceptualized as an interconnected coupled system composed of an edge subsystem (ES) and a node s

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37

Gallas, Jason A. C. "Monogenic period equations are cyclotomic polynomials." International Journal of Modern Physics C 31, no. 04 (2020): 2050058. http://dx.doi.org/10.1142/s0129183120500588.

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We study monogeneity in period equations, [Formula: see text], the auxiliary equations introduced by Gauss to solve cyclotomic polynomials by radicals. All monogenic [Formula: see text] of degrees [Formula: see text] are determined for extended intervals of primes [Formula: see text], and found to coincide either with cyclotomic polynomials or with simple de Moivre reduced forms of cyclotomic polynomials. The former case occurs for [Formula: see text], and the latter for [Formula: see text]. For [Formula: see text], we conjecture all monogenic period equations to be cyclotomic polynomials. Tot

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38

Ene, Remus-Daniel, Nicolina Pop, Marioara Lapadat, and Luisa Dungan. "Approximate Closed-Form Solutions for the Maxwell-Bloch Equations via the Optimal Homotopy Asymptotic Method." Mathematics 10, no. 21 (2022): 4118. http://dx.doi.org/10.3390/math10214118.

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This paper emphasizes some geometrical properties of the Maxwell–Bloch equations. Based on these properties, the closed-form solutions of their equations are established. Thus, the Maxwell–Bloch equations are reduced to a nonlinear differential equation depending on an auxiliary unknown function. The approximate analytical solutions were built using the optimal homotopy asymptotic method (OHAM). These represent the ε-approximate OHAM solutions. A good agreement between the analytical and corresponding numerical results was found. The accuracy of the obtained results is validated through the re

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Ene, Remus-Daniel, Nicolina Pop, and Rodica Badarau. "Semi-Analytical Solutions for the Qi-Type Dynamical System." Symmetry 16, no. 12 (2024): 1578. http://dx.doi.org/10.3390/sym16121578.

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The aim of present paper is to obtain approximate semi-analytical solutions for the Qi-type dynamical system, while neglecting its chaotic behaviors. These solutions are derived using the Optimal Auxiliary Functions Method (OAFM). The impact of the system’s physical parameters is also investigated. A special case, involving a constant of motion, is considered for which closed-form solutions are obtained. The dynamical system is reduced to a second-order nonlinear differential equation, which is analytically solved through the OAFM procedure. The influence of initial conditions on the system is

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40

Pieschner, Susanne, and Christiane Fuchs. "Bayesian inference for diffusion processes: using higher-order approximations for transition densities." Royal Society Open Science 7, no. 10 (2020): 200270. http://dx.doi.org/10.1098/rsos.200270.

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Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods that introduce auxiliary data. These methods typically approximate the transition densities of the process numerically, both for calculating the posterior densities and proposing auxiliary data. Here, the Euler–Maruyama scheme is the standard approximation technique. However, the MCMC method is computationally expensive. Using higher-order approximations ma

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Nagarajan Krishnamurthy, Et al. "Heavy Vehicles: Distributed Hybrid Power System and Vehicle." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 1 (2023): 185–88. http://dx.doi.org/10.17762/ijritcc.v11i1.9802.

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This research focuses on the development of a distributed hybrid power system and vehicle for heavy vehicles. The dynamical system comprises a power plant module, a drive module, an energy-storage module, and an entire car controller. The power plant module consists of one or more auxiliary power units that provide power to the heavy vehicle's power system. The drive module includes multiple driver elements responsible for directly driving the heavy vehicle's drive axles or operating individual wheels through direct drive. The energy-storage module serves as an energy reserve. The entire car c

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Rubezic, Vesna, and Ana Jovanovic. "Erbium - doped fiber laser systems: Routes to chaos." Serbian Journal of Electrical Engineering 11, no. 4 (2014): 551–63. http://dx.doi.org/10.2298/sjee1404551r.

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Erbium-doped fiber laser systems exhibit a large variety of complex dynamical behaviors, bifurcations and attractors. In this paper, the chaotic behavior which can be achieved under certain conditions in a laser system with erbium-doped fiber, is discussed. The chaos in this system occurs through several standard scenarios. In this paper, the simulation sequence of quasiperiodic, intermittent and period-doubling scenario transitions to chaos is shown. Quasiperiodic and intermittent transitions to chaos are shown on the example system with a single ring. The electro-optical modulator was applie

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Gao, Peitao, Yinhe Wang, Yi Peng, LiLi Zhang, and Shengping Li. "Tracking control of the nodes for the complex dynamical network with the auxiliary links dynamics." Information Sciences 628 (May 2023): 350–59. http://dx.doi.org/10.1016/j.ins.2023.01.124.

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Xie, H., G. T. Flowers, L. Feng, and C. Lawrence. "Steady-State Dynamic Behavior of a Flexible Rotor With Auxiliary Support from a Clearance Bearing." Journal of Vibration and Acoustics 121, no. 1 (1999): 78–83. http://dx.doi.org/10.1115/1.2893951.

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This paper investigates the steady-state responses of a rotor system supported by auxiliary bearings in which there is a clearance between the rotor and the inner race of the bearing. A simulation model based upon the rotor of a production jet engine is developed and its steady-state behavior is explored over a wide range of operating conditions for various parametric configurations. Specifically, the influence of rotor imbalance, clearance, support stiffness and damping is studied. Bifurcation diagrams are used as a tool to examine the dynamic behavior of this system as a function of the afor

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Li, Yang, Qinghua Zhang, Yanwei Xu, Jinlong Wen, and Zhihao Wang. "Performance Evaluation of Inerter-Based Dynamic Vibration Absorbers for Wind-Induced Vibration Control of a Desulfurization Tower." Buildings 14, no. 1 (2024): 150. http://dx.doi.org/10.3390/buildings14010150.

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High-rise flue gas desulfurization towers are susceptible to wind loads, which can cause instability and failure in the along-wind and across-wind directions. The tuned mass damper (TMD) has been widely applied in the wind-induced vibration control of high-rise structures. To enhance the control performance and reduce the auxiliary mass of TMD, this study focuses on inerter-based dynamic vibration absorbers (IDVAs) for controlling the vibration response of a desulfurization tower. The dynamical equations of the tower–IDVA systems are established under wind loads, and a parameter optimization s

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Liu, Lizhi, Cao Chen, Zilin Gao, and Bo Cheng. "Cluster synchronization for controlled nodes via the dynamics of edges in complex dynamical networks." PLOS ONE 18, no. 8 (2023): e0288657. http://dx.doi.org/10.1371/journal.pone.0288657.

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An appropriate dynamic coupling form between nodes and edges’ state can effectively promote the emergence of desired network function (phenomenon), but the existing literatures have not conducted in-depth research on the coupling mechanism. This paper mainly focuses on the coupling auxiliary mechanism of dynamic edges for the emergence of cluster phenomenon of nodes, explores the essential relation between structure and function in complex dynamical networks (CDNs). Firstly, a novel model of CDNs has dynamic systems attached on not only nodes but also edges is proposed from the viewpoint of la

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Krishnan, Giri P., Gregory Filatov, Andrey Shilnikov, and Maxim Bazhenov. "Electrogenic properties of the Na+/K+ATPase control transitions between normal and pathological brain states." Journal of Neurophysiology 113, no. 9 (2015): 3356–74. http://dx.doi.org/10.1152/jn.00460.2014.

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Ionic concentrations fluctuate significantly during epileptic seizures. In this study, using a combination of in vitro electrophysiology, computer modeling, and dynamical systems analysis, we demonstrate that changes in the potassium and sodium intra- and extracellular ion concentrations ([K+] and [Na+], respectively) during seizure affect the neuron dynamics by modulating the outward Na+/K+pump current. First, we show that an increase of the outward Na+/K+pump current mediates termination of seizures when there is a progressive increase in the intracellular [Na+]. Second, we show that the Na+

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Klus, Stefan, Feliks Nüske, and Boumediene Hamzi. "Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator." Entropy 22, no. 7 (2020): 722. http://dx.doi.org/10.3390/e22070722.

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Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions,

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Jansson, Olli, and Matthew W. Harris. "Convex Optimization-Based Techniques for Trajectory Design and Control of Nonlinear Systems with Polytopic Range." Aerospace 10, no. 1 (2023): 71. http://dx.doi.org/10.3390/aerospace10010071.

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This paper presents new techniques for the trajectory design and control of nonlinear dynamical systems. The technique uses a convex polytope to bound the range of the nonlinear function and associates with each vertex an auxiliary linear system. Provided controls associated with the linear systems can be generated to satisfy an ordering constraint, the nonlinear control is computable by the interpolation of controls obtained by convex optimization. This theoretical result leads to two numerical approaches for solving the nonlinear constrained problem: one requires solving a single convex opti

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Gu, Mingxia, Zhiyong Yu, Haijun Jiang, and Da Huang. "Distributed consensus of discrete time-varying linear multi-agent systems with event-triggered intermittent control." Mathematical Biosciences and Engineering 21, no. 1 (2023): 415–43. http://dx.doi.org/10.3934/mbe.2024019.

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<abstract><p>The consensus problem of discrete time-varying linear multi-agent systems (MASs) is studied in this paper. First, an event-triggered intermittent control (ETIC) protocol is designed, aided by a class of auxiliary functions. Under this protocol, some sufficient conditions for all agents to achieve consensus are established by constructing an error dynamical system and applying the Lyapunov function. Second, in order to further reduce the communication burden, an improved event triggered intermittent control (I-ETIC) strategy is presented, along with corresponding conver

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