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Journal articles on the topic 'Linear dynamical system'

Author: Grafiati

Published: 28 May 2022

Last updated: 30 July 2025

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1

Salim Youns, Anas. "STABILITY OF NON-LINEAR DYNAMICAL SYSTEM." International Journal of Advanced Research 9, no. 07 (2021): 275–83. http://dx.doi.org/10.21474/ijar01/13126.

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The mainobjective of this research is to study the stability of thenon-lineardynamical system by using the linearization technique of three dimension systems toobtain an approximate linear system and find its stability. We apply this technique to reaches to the stability of the public non linear dynamical systems of dimension. Finally, some proposed examples (example (1) and example (2)) are given to explain this technique and used the corollary.

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2

Rehman, Mutti-Ur, Jehad Alzabut, and Arfan Hyder. "Quadratic Stability of Non-Linear Systems Modeled with Norm Bounded Linear Differential Inclusions." Symmetry 12, no. 9 (2020): 1432. http://dx.doi.org/10.3390/sym12091432.

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In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed methodology reformulate non-linear differential inclusion to an equivalent non-linear system. Lyapunov function demonstrate the existence of a symmetric positive definite matrix to analyze the stability of non-linear dynamical systems. The proposed method allows us to construct a system of ordinary differential equations to localize the spectrum o

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3

Zaksienė, Genovaitė. "The decay of mechanical oscillations in piecewise linear system." Lietuvos matematikos rinkinys 44 (December 17, 2004): 779–83. http://dx.doi.org/10.15388/lmr.2004.32264.

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The application of the dynamical dampers in the mechanical systems, when the sources of stimulation are impossible to abolish, is one of the ways to fight against the harmful vibrations. The linear dynamical damper of nonlinear systems can compensate the force of stimulation in wide diapason of frequency. The parameters of dynamical system where dynamical damper exists more effectively are determined.

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4

Cong, Nguyen Dinh. "Structural stability of linear random dynamical systems." Ergodic Theory and Dynamical Systems 16, no. 6 (1996): 1207–20. http://dx.doi.org/10.1017/s0143385700009998.

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AbstractIn this paper, structural stability of discrete-time linear random dynamical systems is studied. A random dynamical system is called structurally stable with respect to a random norm if it is topologically conjugate to any random dynamical system which is sufficiently close to it in this norm. We prove that a discrete-time linear random dynamical system is structurally stable with respect to its Lyapunov norms if and only if it is hyperbolic.

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5

Chen, Yongxin, Tryphon T. Georgiou, and Michele Pavon. "Optimal Transport Over a Linear Dynamical System." IEEE Transactions on Automatic Control 62, no. 5 (2017): 2137–52. http://dx.doi.org/10.1109/tac.2016.2602103.

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6

Mendelson, Kenneth S., and Frank G. Karioris. "Chaoticlike motion of a linear dynamical system." American Journal of Physics 59, no. 3 (1991): 221–24. http://dx.doi.org/10.1119/1.16566.

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7

Song, Yang, Chong Xiao Wang, and Wee Peng Tay. "Compressive Privacy for a Linear Dynamical System." IEEE Transactions on Information Forensics and Security 15 (2020): 895–910. http://dx.doi.org/10.1109/tifs.2019.2930366.

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8

Nakamura, Akira, and Nozomu Hamada. "Identification of nonlinear dynamical system by piecewise-linear system." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 74, no. 9 (1991): 102–15. http://dx.doi.org/10.1002/ecjc.4430740911.

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9

Hui, Qing, and Wassim M. Haddad. "Semistability of switched dynamical systems, Part I: Linear system theory." Nonlinear Analysis: Hybrid Systems 3, no. 3 (2009): 343–53. http://dx.doi.org/10.1016/j.nahs.2009.02.003.

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10

IMAMURA, Hitoshi. "425 Formulation of Piecewise Linear System by Integrable Dynamical System." Proceedings of the Dynamics & Design Conference 2003 (2003): _425–1_—_425–6_. http://dx.doi.org/10.1299/jsmedmc.2003._425-1_.

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11

Jin Huan, and Li Chuandong. "Chaotification of Linear Dynamical System via Impulsive Control." International Journal of Information Processing and Management 2, no. 3 (2011): 27–33. http://dx.doi.org/10.4156/ijipm.vol2.issue3.4.

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12

Z., J. M., and Tong Howell. "Non Linear Time Series. A Dynamical System Approach." Population (French Edition) 47, no. 5 (1992): 1320. http://dx.doi.org/10.2307/1533949.

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13

Stine, Robert A., and Howell Tong. "Non-linear Time Series: A Dynamical System Approach." Journal of the American Statistical Association 87, no. 419 (1992): 903. http://dx.doi.org/10.2307/2290240.

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14

Goldenstein, Siome, Edward Large, and Dimitris Metaxas. "Non-linear dynamical system approach to behavior modeling." Visual Computer 15, no. 7-8 (1999): 349–64. http://dx.doi.org/10.1007/s003710050184.

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15

Chernous'ko, F. L. "Control synthesis in a non-linear dynamical system." Journal of Applied Mathematics and Mechanics 56, no. 2 (1992): 157–66. http://dx.doi.org/10.1016/0021-8928(92)90068-j.

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16

Li, Yang, Junyuan Hong, and Huanhuan Chen. "Short Sequence Classification Through Discriminable Linear Dynamical System." IEEE Transactions on Neural Networks and Learning Systems 30, no. 11 (2019): 3396–408. http://dx.doi.org/10.1109/tnnls.2019.2891743.

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17

Nagaraj, Nithin, Prabhakar G. Vaidya, and Kishor G. Bhat. "Arithmetic coding as a non-linear dynamical system." Communications in Nonlinear Science and Numerical Simulation 14, no. 4 (2009): 1013–20. http://dx.doi.org/10.1016/j.cnsns.2007.12.001.

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18

GAIKO, VALERY A., and WIM T. VAN HORSSEN. "A PIECEWISE LINEAR DYNAMICAL SYSTEM WITH TWO DROPPING SECTIONS." International Journal of Bifurcation and Chaos 19, no. 04 (2009): 1367–72. http://dx.doi.org/10.1142/s021812740902369x.

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In this paper, we consider a planar dynamical system with a piecewise linear function containing two dropping sections and approximating some continuous nonlinear function. Studying all possible local and global bifurcations of its limit cycles, we prove that such a piecewise linear dynamical system, with five singular points, can have at most four limit cycles, three of which surround the foci one by one and the fourth limit cycle surrounds all of the singular points of this system.

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19

Chu, Moody T. "Linear algebra algorithms as dynamical systems." Acta Numerica 17 (April 25, 2008): 1–86. http://dx.doi.org/10.1017/s0962492906340019.

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Any logical procedure that is used to reason or to infer either deductively or inductively, so as to draw conclusions or make decisions, can be called, in a broad sense, a realization process. A realization process usually assumes the recursive form that one state develops into another state by following a certain specific rule. Such an action is generally formalized as a dynamical system. In mathematics, especially for existence questions, a realization process often appears in the form of an iterative procedure or a differential equation. For years researchers have taken great effort to desc

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20

Escalante-González, R. J., and E. Campos-Cantón. "Generation of chaotic attractors without equilibria via piecewise linear systems." International Journal of Modern Physics C 28, no. 01 (2017): 1750008. http://dx.doi.org/10.1142/s0129183117500085.

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In this paper, we present a mechanism of generation of a class of switched dynamical system without equilibrium points that generates a chaotic attractor. The switched dynamical systems are based on piecewise linear (PWL) systems. The theoretical results are formally given through a theorem and corollary which give necessary and sufficient conditions to guarantee that a linear affine dynamical system has no equilibria. Numerical results are in accordance with the theory.

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21

Zenger, K., and R. Ylinen. "Representations With Constant System Matrices of Linear Time-Periodic Dynamical Systems." IFAC Proceedings Volumes 41, no. 2 (2008): 11486–90. http://dx.doi.org/10.3182/20080706-5-kr-1001.01946.

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22

Koga, S., and S. Akiyama. "Instability of Quasi-Linear Hyperbolic Systems: The Hamiltonian Dynamical System Approach." Progress of Theoretical Physics 79, no. 5 (1988): 991–96. http://dx.doi.org/10.1143/ptp.79.991.

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23

Hui, Qing, and Wassim M. Haddad. "Semistability of switched dynamical systems, Part II: Non-linear system theory." Nonlinear Analysis: Hybrid Systems 3, no. 3 (2009): 354–62. http://dx.doi.org/10.1016/j.nahs.2009.02.004.

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24

Tran, Tuong Manh. "ON A STOCHASTIC LINEAR DYNAMICAL SYSTEM DRIVEN BY A VOLTERRA PROCESS." Journal of Computer Science and Cybernetics 37, no. 2 (2021): 163–70. http://dx.doi.org/10.15625/1813-9663/37/2/15340.

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The aim of this note is considering a dynamical system expressed by a Langevin equation driven by a Volterra process. An Ornstein - Uhlenbeck process as the solution of this kind of equation is described and a problem of state estimation (filtering) for this dynamical system is investigated as well.

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25

Ibrahim, Mohammed K., Taha Rabeh, and Elbaz I. Abouelmagd. "Dynamical Properties of Perturbed Hill’s System." Mathematical and Computational Applications 29, no. 4 (2024): 66. http://dx.doi.org/10.3390/mca29040066.

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In this work, some dynamical properties of Hill’s system are studied under the effect of continued fraction perturbation. The locations and kinds of equilibrium points are identified, and it is demonstrated that these points are saddle points and the general motion in their proximity is unstable. Furthermore, the curves of zero velocity and the regions of possible motion are defined at different Jacobian constant values. It is shown that the regions of forbidden motion increase with increasing Jacobian constant values and there is a noticeable decrease in the permissible regions of motion, lea

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26

Ivanyi, Amalia, Peter Ivanyi, Miklos M. Ivanyi, and Miklos Ivanyi. "A Periodical Loaded Dynamical System." Materials Science Forum 721 (June 2012): 301–6. http://dx.doi.org/10.4028/www.scientific.net/msf.721.301.

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In the paper a Preisach hysteresis model is applied to determine the dynamic behavior of a steel column with a mass on the top and loaded by periodically alternating force. The column is considered as a completely rigid element, while the fixed end of the column is modeled with a rotational spring with hysteresis characteristic. In the solution of the non-linear dynamical equation of the motion the fix-point technique is inserted to the time marching iteration. The cycling time of the force is changing. The results are plotted in figures.

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27

Pandit, Purnima K. "Exact Solution of Semi-linear Fuzzy System." Journal of the Indian Mathematical Society 84, no. 3-4 (2017): 225. http://dx.doi.org/10.18311/jims/2017/15569.

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In this paper we consider a semi-linear dynamical system with fuzzy initial condition. We discuss the results regarding the existence of the solution and obtain the best possible solution for such systems. We give a real life supportive illustration of population model, justify the need for fuzzy setup for the problem, and discuss the solution for it.

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28

López-Caamal, Fernando, and Ixbalank Torres Zúñiga. "Gradient Estimate for Continuous-Time Linear Dynamical Systems." Memorias del Congreso Nacional de Control Automático 7, no. 1 (2024): 434–38. https://doi.org/10.58571/cnca.amca.2024.074.

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In this paper we compare two different methodologies for computing the gradient of a linear, continuous-time dynamical system with no parametric uncertainties nor unknown inputs. Such a gradient is computed by performing the partial derivative of a performance function w.r.t. the input of the system. The first of the methodologies uses the model of the dynamical system to construct the gradient; whereas the second one avails of the differentiation of the performance function and the system’s input. We compare both approaches via a numerical simulation.

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29

KUMON, Toshiro, Tatsuya SUZUKI, Makoto IWASAKI, Tomonori HASIYAMA, Nobuyuki MATSUI, and Shigeru OKUMA. "System Identification for Structure-Unknown Linear Dynamical System by Evolutionary Computation." Transactions of the Society of Instrument and Control Engineers 36, no. 11 (2000): 995–1002. http://dx.doi.org/10.9746/sicetr1965.36.995.

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30

Ghane, Hamed, Alef E. Sterk, and Holger Waalkens. "Chaotic dynamics from a pseudo-linear system." IMA Journal of Mathematical Control and Information 37, no. 2 (2019): 377–94. http://dx.doi.org/10.1093/imamci/dnz005.

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Abstract Investigating the possibility of applying techniques from linear systems theory to the setting of non-linear systems has been the focus of many papers. The pseudo-linear (PL) form representation of non-linear dynamical systems has led to the concept of non-linear eigenvalues (NEValues) and non-linear eigenvectors (NEVectors). When the NEVectors do not depend on the state vector of the system, then the NEValues determine the global qualitative behaviour of a non-linear system throughout the state space. The aim of this paper is to use this fact to construct a non-linear dynamical syste

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31

Khan, Ayub, and Prempal Singh. "Non Linear Dynamical Systems and Chaos Synchronization." International Journal of Artificial Life Research 1, no. 2 (2010): 43–57. http://dx.doi.org/10.4018/jalr.2010040104.

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In this paper, the authors study chaos synchronization of chaotic systems, which can exhibit a two scroll attractor for different parameter values via linear feedback control. First, chaos synchronization of three dimensional systems is studied and ‘generalized non-linear dynamical systems’ are analyzed. The considered synchronization criterion consists of identical drive and response systems coupled with linear state error variables. As a consequence, the authors have proposed some theorems for synchronization. This paper features sufficient synchronization criteria for the linear coupled gen

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32

Roy, Tamal, Ranjit Kumar Barai, and Rajeeb Dey. "H∞ control oriented LFT modelling of linear dynamical system." Advances in Modelling and Analysis C 73, no. 4 (2018): 189–96. http://dx.doi.org/10.18280/ama_c.730408.

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33

Thi, Ngoc Anh Nguyen, Hyung-Jeong Yang, Soo-Hyung Kim, Guee-Sang Lee, and Sun-Hee Kim. "Improved Linear Dynamical System for Unsupervised Time Series Recognition." International Journal of Contents 10, no. 1 (2014): 47–53. http://dx.doi.org/10.5392/ijoc.2013.10.1.047.

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34

Poria, Swarup, and Ömür Umut. "Chaos Synchronization of Lü Dynamical System via Linear Transformations." Journal of Dynamical Systems and Geometric Theories 4, no. 1 (2006): 87–93. http://dx.doi.org/10.1080/1726037x.2006.10698505.

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35

Gopalakrishnan, Viswanath, Deepu Rajan, and Yiqun Hu. "A Linear Dynamical System Framework for Salient Motion Detection." IEEE Transactions on Circuits and Systems for Video Technology 22, no. 5 (2012): 683–92. http://dx.doi.org/10.1109/tcsvt.2011.2177177.

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36

Masterkov, Yu V., and L. I. Rodina. "Controllability of a linear dynamical system with random parameters." Differential Equations 43, no. 4 (2007): 469–77. http://dx.doi.org/10.1134/s0012266107040040.

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37

Tan, Yue, Chunjing Hu, Kuan Zhang, Kan Zheng, Ethan A. Davis, and Jae Sung Park. "LSTM-Based Anomaly Detection for Non-Linear Dynamical System." IEEE Access 8 (2020): 103301–8. http://dx.doi.org/10.1109/access.2020.2999065.

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38

Stark, Jaroslav. "Non-linear Series: A Dynamical System Approach (Howell Tong)." SIAM Review 34, no. 1 (1992): 149–51. http://dx.doi.org/10.1137/1034036.

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39

Fujiwara, Ren, Yasuko Matsubara, and Yasushi Sakurai. "Modeling Latent Non-Linear Dynamical System over Time Series." Proceedings of the AAAI Conference on Artificial Intelligence 39, no. 11 (2025): 11663–71. https://doi.org/10.1609/aaai.v39i11.33269.

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We study the problem of modeling a non-linear dynamical system when given a time series by deriving equations directly from the data. Despite the fact that time series data are given as input, models for dynamics and estimation algorithms that incorporate long-term temporal dependencies are largely absent from existing studies. In this paper, we introduce a latent state to allow time-dependent modeling and formulate this problem as a dynamics estimation problem in latent states. We face multiple technical challenges, including (1) modeling latent non-linear dynamics and (2) solving circular de

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40

Wang, Hongli, Bing Tan, Xiaohua Gao, and Enmin Feng. "The Strong Stability of Optimal Nonlinear Dynamical System in Batch Fermentation." Journal of Mathematics 2022 (November 16, 2022): 1–8. http://dx.doi.org/10.1155/2022/2206419.

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For the bio-dissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae, the nonlinear dynamical system of the complex metabolism in microbial batch fermentation is studied in this study. Since the analytical solution and equilibrium point cannot be found for the nonlinear dynamical system of batch fermentation, the system stability cannot be analyzed using general methods. Therefore, in this study, the stability of the system is analyzed from another angle. We present the corresponding linear variational system for the solution to the nonlinear dynamical system of complex metabolism

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41

Bhaskara, Ramchander Rao, Manoranjan Majji, and Felipe Guzmán. "Quantized State Estimation for Linear Dynamical Systems." Sensors 24, no. 19 (2024): 6381. http://dx.doi.org/10.3390/s24196381.

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This paper investigates state estimation methods for dynamical systems when model evaluations are performed on resource-constrained embedded systems with finite precision compute elements. Minimum mean square estimation algorithms are reformulated to incorporate finite-precision numerical errors in states, inputs, and measurements. Quantized versions of least squares batch estimation, sequential Kalman, and square-root filtering algorithms are proposed for fixed-point implementations. Numerical simulations are used to demonstrate performance improvements over standard filter formulations. Stea

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42

MIYAZAKI, SYUJI, and YASUSHI NAGASHIMA. "NETWORK AS A CHAOTIC DYNAMICAL SYSTEM." International Journal of Bifurcation and Chaos 17, no. 10 (2007): 3529–33. http://dx.doi.org/10.1142/s0218127407019317.

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A directed network such as the WWW can be represented by a transition matrix. Comparing this matrix to a Frobenius–Perron matrix of a chaotic piecewise-linear one-dimensional map whose domain can be divided into Markov subintervals, we are able to relate the network structure itself to chaotic dynamics. Just like various large deviation properties of local expansion rates (finite-time Lyapunov exponents) related to chaotic dynamics, we can also discuss those properties of network structure.

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43

Johnson, C. D. "New results on the inverse-system/deconvolution problem for linear dynamical systems." Circuits Systems and Signal Processing 19, no. 4 (2000): 365–83. http://dx.doi.org/10.1007/bf01200893.

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44

Cheng, Sen, and Philip N. Sabes. "Modeling Sensorimotor Learning with Linear Dynamical Systems." Neural Computation 18, no. 4 (2006): 760–93. http://dx.doi.org/10.1162/neco.2006.18.4.760.

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Recent studies have employed simple linear dynamical systems to model trial-by-trial dynamics in various sensorimotor learning tasks. Here we explore the theoretical and practical considerations that arise when employing the general class of linear dynamical systems (LDS) as a model for sensorimotor learning. In this framework, the state of the system is a set of parameters that define the current sensorimotor transformation— the function that maps sensory inputs to motor outputs. The class of LDS models provides a first-order approximation for any Markovian (state-dependent) learning rule tha

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45

Menh, Nguyen Cao, and Tran Duong Tri. "The balancing of rotating machinery as non-linear system passing across a resonant region." Vietnam Journal of Mechanics 25, no. 4 (2003): 225–42. http://dx.doi.org/10.15625/0866-7136/25/4/6594.

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This paper presents a dynamical balancing method for the rotational part of machine as a nonlinear system with the decrease of rotation speed passing across a resonant region. After analyzing the nonlinear system and measurable vibration signals, a suitable procedure of dynamical balance for determining the magnitude and location of imbalance mass is proposed. A program on PC is made to illustrate the obtained procedure. The results of numeric examples show that it can be used well for dynamical balancing analysis.

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46

Deng, Zi-Hao. "Analysis and control of financial stability based on non-linear differential dynamical systems." Thermal Science 29, no. 3 Part A (2025): 1783–92. https://doi.org/10.2298/tsci2503783d.

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As a complex system with multi-body interactions, the financial market functions in accordance with the non-linear differential dynamical system characteristics and properties. Although the financial market is a complex system with multiple constraints and perturbations, it is subject to a number of universal laws. This paper introduces fractional-order non-linear differential dynamical systems as a means of modeling and analyzing financial stability, as well as exploring the dynamical characteristics and large-time behavior of complex financial systems. Empirical simulation analysis and testi

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47

Hinich, Melvin J. "SAMPLING DYNAMICAL SYSTEMS." Macroeconomic Dynamics 3, no. 4 (1999): 602–9. http://dx.doi.org/10.1017/s1365100599013073.

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Linear dynamical systems are widely used in many different fields from engineering to economics. One simple but important class of such systems is called the single-input transfer function model. Suppose that all variables of the system are sampled for a period using a fixed sample rate. The central issue of this paper is the determination of the smallest sampling rate that will yield a sample that will allow the investigator to identify the discrete-time representation of the system. A critical sampling rate exists that will identify the model. This rate, called the Nyquist rate, is twice the

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48

BAO, BOCHENG, JIANPING XU, ZHONG LIU, and ZHENGHUA MA. "HYPERCHAOS FROM AN AUGMENTED LÜ SYSTEM." International Journal of Bifurcation and Chaos 20, no. 11 (2010): 3689–98. http://dx.doi.org/10.1142/s0218127410027969.

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This letter introduces a hyperchaotic system from the Lü system [Lü et al., 2004] with a linear state feedback controller. This hyperchaotic system has more complex dynamical behaviors, and can generate 4-scroll hyperchaotic attractor and 2-scroll chaotic attractor under different control parameters. In particular, the system can also exhibit novel coexisting intermittent chaotic orbits. Theoretical analyses and simulation experiments are conducted to investigate the dynamical behaviors of the proposed hyperchaotic system.

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49

Teplinsky, Yu. "ON APPROXIMATION OF ALMOST-PERIODIC SOLUTIONS FOR A NON-LINEAR COUNTABLE SYSTEM OF DIFFERENTIAL EQUATIONS BY QUASI-PERIODIC SOLUTIONS FOR SOME LINEAR SYSTEM." Bukovinian Mathematical Journal 9, no. 2 (2021): 111–23. http://dx.doi.org/10.31861/bmj2021.02.09.

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It is well-known that many applied problems in diﬀerent areas of mathematics, physics, and technology require research into questions of existence of oscillating solutions for diﬀerential systems, which are their mathematical models. This is especially true for the problems of celestial mechanics. Novadays, by oscillatory motions in dynamical systems, according to V. V. Nemitsky, we call their recurrent motions. As it is known from Birkhoﬀ theorem, trajectories of such motions contain minimal compact sets of dynamical systems. The class of recurrent motions contains, in particular, both quasi-

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50

Arieşanu, Camelia Pop. "Stability Problems for Chua System with One Linear Control." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/764108.

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A Hamilton-Poisson realization and some stability problems for a dynamical system arisen from Chua system are presented. The stability and dynamics of a linearized smooth version of the Chua system are analyzed using the Hamilton-Poisson formalism. This geometrical approach allows to deduce the nonlinear stabilization near different equilibria.

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