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Journal articles on the topic 'Chen system'

Author: Grafiati

Published: 28 June 2021

Last updated: 29 July 2025

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1

Llibre, Jaume, and Ana Rodrigues. "On the Dynamics of the Unified Chaotic System Between Lorenz and Chen Systems." International Journal of Bifurcation and Chaos 25, no. 09 (2015): 1550122. http://dx.doi.org/10.1142/s0218127415501229.

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A one-parameter family of differential systems that bridges the gap between the Lorenz and the Chen systems was proposed by Lu, Chen, Cheng and Celikovsy. The goal of this paper is to analyze what we can say using analytic tools about the dynamics of this one-parameter family of differential systems. We shall describe its global dynamics at infinity, and for two special values of the parameter a we can also describe the global dynamics in the whole ℝ3using the invariant algebraic surfaces of the family. Additionally we characterize the Hopf bifurcations of this family.

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2

Inagi, Shinsuke, Yulin Shi, Elena Villani, and Guobao Xu. "Electropolymerization of Pyrrole Using a Single-Electrode Electrochemical System." ECS Meeting Abstracts MA2024-01, no. 41 (2024): 2339. http://dx.doi.org/10.1149/ma2024-01412339mtgabs.

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Bipolar electrochemistry emerges as an appealing technique for gradient surface fabrication thanks to the controllable potential distribution on bipolar electrodes (BPEs) in a wireless manner [1]. Here we report a BPE array named the single-electrode electrochemical system (SEES) [2] for the high-throughput electrosynthesis of gradient polypyrrole (PPy) films via electropolymerization. The SEES consists of a plastic board with holes attached to an indium-tin oxide (ITO) electrode to create multiple microelectrochemical cell arrays. Benefiting from this technique, the effects of various electro

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3

ELABBASY, E. M., H. N. AGIZA, and M. M. EL-DESSOKY. "SYNCHRONIZATION OF MODIFIED CHEN SYSTEM." International Journal of Bifurcation and Chaos 14, no. 11 (2004): 3969–79. http://dx.doi.org/10.1142/s0218127404011740.

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This paper addresses the synchronization problem of two modified Chen systems in the presence of unknown system parameters. One-way coupling and active control laws are applied to achieve the state synchronization of two identical modified Chen systems. Based on Lyapunov stability theory, active control laws are derived such that the two modified Chen systems are to be synchronized. Numerical simulations results are used to demonstrate the effectiveness of the proposed control methods.

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4

Huang, Qiujian, Aimin Liu, and Yongjian Liu. "Jacobi Stability Analysis of the Chen System." International Journal of Bifurcation and Chaos 29, no. 10 (2019): 1950139. http://dx.doi.org/10.1142/s0218127419501396.

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In this paper, the research of the Jacobi stability of the Chen system is performed by using the KCC-theory. By associating a nonlinear connection and a Berwald connection, five geometrical invariants of the Chen system are obtained. The Jacobi stability of the Chen system at equilibrium points and a periodic orbit is investigated in terms of the eigenvalues of the deviation curvature tensor. The obtained results show that the origin is always Jacobi unstable, while the Jacobi stability of the other two nonzero equilibrium points depends on the values of the parameters. And a periodic orbit of

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5

LÜ, JINHU, GUANRONG CHEN, DAIZHAN CHENG, and SERGEJ CELIKOVSKY. "BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM." International Journal of Bifurcation and Chaos 12, no. 12 (2002): 2917–26. http://dx.doi.org/10.1142/s021812740200631x.

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This paper introduces a unified chaotic system that contains the Lorenz and the Chen systems as two dual systems at the two extremes of its parameter spectrum. The new system represents the continued transition from the Lorenz to the Chen system and is chaotic over the entire spectrum of the key system parameter. Dynamical behaviors of the unified system are investigated in somewhat detail.

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6

MA, CHAO, and XINGYUAN WANG. "BRIDGE BETWEEN THE HYPERCHAOTIC LORENZ SYSTEM AND THE HYPERCHAOTIC CHEN SYSTEM." International Journal of Modern Physics B 25, no. 05 (2011): 711–21. http://dx.doi.org/10.1142/s0217979211057967.

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This paper presents a novel unified hyperchaotic system that contains the hyperchaotic Lorenz system and the hyperchaotic Chen system as two dual systems at the two extremes of its parameter spectrum. The new system is hyperchaotic over almost the whole range of the system parameter and continuously transfers from the hyperchaotic Lorenz system to the hyperchaotic Chen system. The new findings are not only demonstrated by computer simulations but also verified with bifurcation analysis, Lyapunov exponents and Lyapunov dimension.

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7

Aminikhah, H., A. Refahi Sheikhani, and H. Rezazadeh. "Stability Analysis of Distributed Order Fractional Chen System." Scientific World Journal 2013 (2013): 1–13. http://dx.doi.org/10.1155/2013/645080.

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We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results.

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8

Zheng, Jie, Shao Juan Ma, and Duan Dong. "Chaos Control of the Fractional Order Stochastic Chen System." Advanced Materials Research 694-697 (May 2013): 2130–33. http://dx.doi.org/10.4028/www.scientific.net/amr.694-697.2130.

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In this paper, we study chaos control of the fractional order Chen system with the bounded random parameter. Firstly, we transform the fractional order Chen system with random parameter into an equivalent deterministic system by the orthogonal polynomial approximation. Secondly, based on Routh-Hrwitz criterion, the derivative feedback control laws are applied to fractional order equivalent deterministic Chen system. Lastly, numerical simulations show that the control method is effective and feasible.

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9

WANG, XINGYUAN, MIN XU, and HUAGUANG ZHANG. "TWO ADAPTIVE SYNCHRONIZATION METHODS OF UNCERTAIN CHEN SYSTEM." International Journal of Modern Physics B 23, no. 26 (2009): 5163–69. http://dx.doi.org/10.1142/s0217979209053527.

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This article addresses the adaptive synchronization problem of two Chen systems with uncertain parameters. Two adaptive synchronization methods are designed. In the two methods, we use only two controllers to synchronize uncertain Chen systems. It is theoretically proved that these two methods can make uncertain Chen systems asymptotically synchronized and identify the unknown parameters. Numerical simulations show the effectiveness of the proposed methods further. The comparisons of these two methods show: The method of theorem 1 is easier and more feasible than that of theorem 2, and the syn

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10

WANG, XINGYUAN, and XIANGJUN WU. "PARAMETER IDENTIFICATION AND ADAPTIVE SYNCHRONIZATION OF UNCERTAIN HYPERCHAOTIC CHEN SYSTEM." International Journal of Modern Physics B 22, no. 08 (2008): 1015–23. http://dx.doi.org/10.1142/s0217979208039034.

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This paper studies the adaptive synchronization and parameter identification of an uncertain hyperchaotic Chen system. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical hyperchaotic Chen systems asymptotically synchronized. With this approach, the synchronization and parameter identification of the hyperchaotic Chen system with five uncertain parameters can be achieved simultaneously. Theoretical proof and numerical simulations demonstrate the effectiveness and feasibility of the proposed scheme.

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11

Li, Yin, and Chun-long Zheng. "The Complex Network Synchronization via Chaos Control Nodes." Journal of Applied Mathematics 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/823863.

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We investigate chaos control nodes of the complex network synchronization. The structure of the coupling functions between the connected nodes is obtained based on the chaos control method and Lyapunov stability theory. Moreover a complex network with nodes of the new unified Loren-Chen-Lü system, Coullet system, Chee-Lee system, and the New system is taken as an example; numerical simulations are used to verify the effectiveness of the method.

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12

HOU, ZHENTING, NING KANG, XIANGXING KONG, GUANRONG CHEN, and GUOJUN YAN. "ON THE NONEQUIVALENCE OF LORENZ SYSTEM AND CHEN SYSTEM." International Journal of Bifurcation and Chaos 20, no. 02 (2010): 557–60. http://dx.doi.org/10.1142/s0218127410025612.

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13

Zhang, Duan, Ao Zhao, XuHua Yang, Ying Sun, and Jie Xiao. "Generalized Synchronization Between Chen System and Rucklidge System." IEEE Access 7 (2019): 8519–26. http://dx.doi.org/10.1109/access.2018.2890311.

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14

Wu, Xianyong, Zhi-Hong Guan, Zhengping Wu, and Tao Li. "Chaos synchronization between Chen system and Genesio system." Physics Letters A 364, no. 6 (2007): 484–87. http://dx.doi.org/10.1016/j.physleta.2006.12.031.

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15

Sooraksa, Pitikhate, and Guanrong Chen. "Chen System as a Controlled Weather Model — Physical Principle, Engineering Design and Real Applications." International Journal of Bifurcation and Chaos 28, no. 04 (2018): 1830009. http://dx.doi.org/10.1142/s0218127418300094.

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This paper presents the Chen system as a controlled weather model. Mathematically, the Chen system is dual to the Lorenz system via time reversal. Physically, the Chen system can be viewed as a controlled weather model from the anti-control perspective. This paper illustrates the physical principle of this controlled weather model, and develops an engineering design of the model for real indoor climate (temperature-humidity) regulation, with a perspective on outdoor weather control application.

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16

LÜ, JINHU, TIANSHOU ZHOU, GUANRONG CHEN, and SUOCHUN ZHANG. "LOCAL BIFURCATIONS OF THE CHEN SYSTEM." International Journal of Bifurcation and Chaos 12, no. 10 (2002): 2257–70. http://dx.doi.org/10.1142/s0218127402005819.

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This paper introduces a new practical method for distinguishing chaotic, periodic and quasi-periodic orbits based on a new criterion, and apply it to investigate the local bifurcations of the Chen system. Conditions for supercritical and subcritical bifurcations are obtained, with their parameter domains specified. The analytic results are also verified by numerical simulation studies.

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17

Hadef, Souhila, and Abdelkrim Boukabou. "Control of multi-scroll Chen system." Journal of the Franklin Institute 351, no. 5 (2014): 2728–41. http://dx.doi.org/10.1016/j.jfranklin.2014.01.015.

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18

Deng, Weihua, and Changpin Li. "Synchronization of Chaotic Fractional Chen System." Journal of the Physical Society of Japan 74, no. 6 (2005): 1645–48. http://dx.doi.org/10.1143/jpsj.74.1645.

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19

Liang, Xiyin, and Guoyuan Qi. "Mechanical analysis of Chen chaotic system." Chaos, Solitons & Fractals 98 (May 2017): 173–77. http://dx.doi.org/10.1016/j.chaos.2017.03.021.

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20

Pham, Viet-Thanh, Xiong Wang, Sajad Jafari, Christos Volos, and Tomasz Kapitaniak. "From Wang–Chen System with Only One Stable Equilibrium to a New Chaotic System Without Equilibrium." International Journal of Bifurcation and Chaos 27, no. 06 (2017): 1750097. http://dx.doi.org/10.1142/s0218127417500973.

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Wang–Chen system with only one stable equilibrium as well as the coexistence of hidden attractors has attracted increasing interest due to its striking features. In this work, the effect of state feedback on Wang–Chen system is investigated by introducing a further state variable. It is worth noting that a new chaotic system without equilibrium is obtained. We believe that the system is an interesting example to illustrate the conversion of hidden attractors with one stable equilibrium to hidden attractors without equilibrium.

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21

SHUKLA, RAVI PRAKASH, SANDIPAN MUKHERJEE, and ASHOK KUMAR MITTAL. "COMPARISON OF GENERALIZED COMPETITIVE MODES AND RETURN MAPS FOR CHARACTERIZING DIFFERENT TYPES OF CHAOTIC ATTRACTORS IN CHEN SYSTEM." International Journal of Bifurcation and Chaos 20, no. 03 (2010): 735–48. http://dx.doi.org/10.1142/s0218127410026022.

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The Chen system of equations exhibits Lorenz, Transition, Chen and Transverse 8 type of chaotic attractors depending on the system parameters. Some authors have proposed a generalized competitive mode (GCM) technique to explain the topological difference between the Lorenz attractor and the Chen attractor. In this paper, we show a range of parameter values for which the nature of the topological attractor for the Chen system is not in accordance with that expected from GCM analysis. Instead, we find that return maps can be used to characterize the transition between different types of attracto

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22

Yin, Chuntao. "Chaos Detection of the Chen System with Caputo–Hadamard Fractional Derivative." International Journal of Bifurcation and Chaos 31, no. 01 (2021): 2150016. http://dx.doi.org/10.1142/s0218127421500164.

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In this paper, we investigate the chaotic behaviors of the Chen system with Caputo–Hadamard derivative. First, we construct some practical numerical schemes for the Chen system with Caputo–Hadamard derivative. Then, by means of the variational equation, we estimate the bounds of the Lyapunov exponents for the considered system. Furthermore, we analyze the dynamical evolution of the Chen system with Caputo–Hadamard derivative based on the Lyapunov exponents, and we found that chaos does exist in the considered system. Some phase diagrams and Lyapunov exponent spectra are displayed to verify our

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23

Sundarapandian, Vaidyanathan. "ACTIVE CONTROLLER DESIGN FOR THE OUTPUT REGULATION OF THE WANG-CHEN-YUAN SYSTEM." Electrical & Computer Engineering: An International Journal (ECIJ 1, no. 1 (2012): 1–11. https://doi.org/10.5281/zenodo.3295601.

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In this paper, we design an active controller for regulating the output of the Wang-Chen-Yuan system (2009), which is one of the recently discovered 3-D chaotic systems. For the constant tracking problem, new state feedback control laws have been derived for regulating the output of the Wang-Chen-Yuan system. Numerical simulations using MATLAB are exhibited to validate and demonstrate the usefulness of the active controller design for the output regulation of the Wang-Chen-Yuan system.

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24

Ren, Hai-Peng, Chao Bai, Zhan-Zhan Huang, and Celso Grebogi. "Secure Communication Based on Hyperchaotic Chen System with Time-Delay." International Journal of Bifurcation and Chaos 27, no. 05 (2017): 1750076. http://dx.doi.org/10.1142/s0218127417500766.

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An experimental secure communication method based on the Chen system with time-delay is being proposed in this paper. The Chen system with time-delay is an infinite-dimensional system having more than one positive Lyapunov exponent. The message to be transmitted is encrypted using an hyperchaotic signal generated by the Chen system with time-delay and multishift cipher function. This encryption makes difficult for an eavesdropper to reconstruct the attractor by using time-delay embedding techniques, return map reconstruction, or spectral analysis, consequently, improving the security. Simulati

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25

Wu, Yan-Ping, and Guo-Dong Wang. "Synchronization between Fractional-Order and Integer-Order Hyperchaotic Systems via Sliding Mode Controller." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/151025.

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The synchronization between fractional-order hyperchaotic systems and integer-order hyperchaotic systems via sliding mode controller is investigated. By designing an active sliding mode controller and choosing proper control parameters, the drive and response systems are synchronized. Synchronization between the fractional-order Chen chaotic system and the integer-order Chen chaotic system and between integer-order hyperchaotic Chen system and fractional-order hyperchaotic Rössler system is used to illustrate the effectiveness of the proposed synchronization approach. Numerical simulations coi

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26

Xu, Fei. "A Class of Integer Order and Fractional Order Hyperchaotic Systems via the Chen System." International Journal of Bifurcation and Chaos 26, no. 06 (2016): 1650109. http://dx.doi.org/10.1142/s0218127416501091.

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In this article, we investigate the generation of a class of hyperchaotic systems via the Chen chaotic system using both integer order and fractional order differential equation systems. Based on the Chen chaotic system, we designed a system with four nonlinear ordinary differential equations. For different parameter sets, the trajectory of the system may diverge or display a hyperchaotic attractor with double wings. By linearizing the ordinary differential equation system with divergent trajectory and designing proper switching controls, we obtain a chaotic attractor. Similar phenomenon has a

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27

Ma, Suqi. "Two-Dimensional Manifolds of Controlled Chen System." International Journal of Bifurcation and Chaos 31, no. 05 (2021): 2150122. http://dx.doi.org/10.1142/s0218127421501224.

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We focus on the two-dimensional stable manifold of Chen system. Based on the Chen system, a new system with nonlinear control is put forward, which exhibits brand new dynamical phenomena such as the coexistence of heteroclinic orbits with periodic solutions, or two new attractors. The emergence of manifold surface is found by tangential self-intersection. The two-dimensional unstable manifold of saddle-focus tends to another equilibrium solution asymptotically, the underlying heteroclinic bifurcation and the “twins” unstable manifolds are bulit from two saddle-focus respectively.

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28

Wu, Xianyong, Hao Wu, Zhengrong Yan, and Yuehua Huang. "Chaos Anti-Synchronization between Chen System and Genesio System." OALib 03, no. 07 (2016): 1–5. http://dx.doi.org/10.4236/oalib.1102856.

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29

Wu, Xian Yong, Hao Wu, and Hao Gong. "Chaos Anti-Synchronization between Chen System and Lu System." Applied Mechanics and Materials 631-632 (September 2014): 710–13. http://dx.doi.org/10.4028/www.scientific.net/amm.631-632.710.

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Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

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30

WANG, XING-YUAN, and MING-JUN WANG. "LINEAR GENERALIZED CHAOTIC SYNCHRONIZATION VIA SINGLE CHANNEL." International Journal of Modern Physics B 25, no. 21 (2011): 2879–87. http://dx.doi.org/10.1142/s0217979211101107.

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In this paper, the drive system and the response system can be in a state of linear generalized synchronization via transmitting single signal. By means of a transitional system, the response system is obtained by variable replacement method. Chen system and hyperchaotic Chen system are used as examples in numerical simulations. Simulation results show the effectiveness of the method.

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31

WANG, XIONG, and GUANRONG CHEN. "A GALLERY OF LORENZ-LIKE AND CHEN-LIKE ATTRACTORS." International Journal of Bifurcation and Chaos 23, no. 04 (2013): 1330011. http://dx.doi.org/10.1142/s0218127413300115.

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In this article, three-dimensional autonomous chaotic systems with two quadratic terms, similar to the Lorenz system in their algebraic forms, are studied. An attractor with two clearly distinguishable scrolls similar to the Lorenz attractor is referred to as a Lorenz-like attractor, while an attractor with more intertwine between the two scrolls similar to the Chen attractor is referred to as a Chen-like attractor. A gallery of Lorenz-like attractors and Chen-like attractors are presented. For several different families of such systems, through tuning only one real parameter gradually, each o

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32

Chen, Cheng-Wu, Ken Yeh, Kevin FR Liu, and Meng-Lung Lin. "RETRACTED: Applications of fuzzy control to nonlinear time-delay systems using the linear matrix inequality fuzzy Lyapunov method." Journal of Vibration and Control 18, no. 10 (2011): 1561–74. http://dx.doi.org/10.1177/1077546311410765.

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In 2013 the Editor of Journal of Vibration and Control and SAGE became aware of a peer review ring involving assumed and fabricated identities that appeared to centre around Peter Chen at National Pingtung University of Education, Taiwan (NPUE). SAGE and the Editor then began a complex investigation into the case during the rest of 2013 and 2014. Following an unsatisfactory response from Peter Chen, NPUE was notified. NPUE were serious in addressing the Journal and SAGE’s concerns. NPUE confirmed that the institution was investigating Peter Chen. SAGE subsequently uncovered a citation ring inv

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33

Cang, Shijian, Aiguo Wu, Zenghui Wang, and Zengqiang Chen. "Distinguishing Lorenz and Chen Systems Based Upon Hamiltonian Energy Theory." International Journal of Bifurcation and Chaos 27, no. 02 (2017): 1750024. http://dx.doi.org/10.1142/s0218127417500249.

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Solving the linear first-order Partial Differential Equations (PDEs) derived from the unified Lorenz system, it is found that there is a unified Hamiltonian (energy function) for the Lorenz and Chen systems, and the unified energy function shows a hyperboloid of one sheet for the Lorenz system and an ellipsoidal surface for the Chen system in three-dimensional phase space, which can be used to explain that the Lorenz system is not equivalent to the Chen system. Using the unified energy function, we obtain two generalized Hamiltonian realizations of these two chaotic systems, respectively. More

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34

BASHKIRTSEVA, IRINA, GUANRONG CHEN, and LEV RYASHKO. "ANALYSIS OF STOCHASTIC CYCLES IN THE CHEN SYSTEM." International Journal of Bifurcation and Chaos 20, no. 05 (2010): 1439–50. http://dx.doi.org/10.1142/s0218127410026587.

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We study the stochastically forced Chen system in its parameter zone under the transition to chaos via period-doubling bifurcations. We suggest a stochastic sensitivity function technique for the analysis of stochastic cycles. We show that this approach allows to construct the dispersion ellipses of random trajectories for any Poincaré sections, and these ellipses reflect the essential features of a spatial arrangement of random trajectories near deterministic cycles. For the Chen system, we demonstrate a growth of stochastic sensitivity of the forced cycles under transition to chaos.

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35

LLIBRE, JAUME, MARCELO MESSIAS, and PAULO RICARDO DA SILVA. "GLOBAL DYNAMICS IN THE POINCARÉ BALL OF THE CHEN SYSTEM HAVING INVARIANT ALGEBRAIC SURFACES." International Journal of Bifurcation and Chaos 22, no. 06 (2012): 1250154. http://dx.doi.org/10.1142/s0218127412501544.

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In this paper, we perform a global analysis of the dynamics of the Chen system [Formula: see text] where (x, y, z) ∈ ℝ3 and (a, b, c) ∈ ℝ3. We give the complete description of its dynamics on the sphere at infinity. For six sets of the parameter values, the system has invariant algebraic surfaces. In these cases, we provide the global phase portrait of the Chen system and give a complete description of the α- and ω-limit sets of its orbits in the Poincaré ball, including its boundary 𝕊2, i.e. in the compactification of ℝ3 with the sphere 𝕊2 of infinity. Moreover, combining the analytical resul

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36

Sprott, J. C., Xiong Wang, and Guanrong Chen. "When Two Dual Chaotic Systems Shake Hands." International Journal of Bifurcation and Chaos 24, no. 06 (2014): 1450086. http://dx.doi.org/10.1142/s0218127414500862.

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This letter reports an interesting finding that the parametric Lorenz system and the parametric Chen system "shake hands" at a particular point of their common parameter space, as the time variable t → +∞ in the Lorenz system while t → -∞ in the Chen system. This helps better clarify and understand the relationship between these two closely related but topologically nonequivalent chaotic systems.

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37

She, Xin Ping. "Two Synchronization Schemes for Chen Chaotic System." Applied Mechanics and Materials 385-386 (August 2013): 915–18. http://dx.doi.org/10.4028/www.scientific.net/amm.385-386.915.

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This paper presents two novel synchronization schemes for Chen chaotic system, drive-response synchronization and adaptive synchronization with unknown parameters, numerical simulation results demonstrate the effectiveness of the proposed method.

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38

CHEN, SHYI-MING, YUN-HOU HUANG, and RUNG-CHING CHEN. "A RECOMMENDATION SYSTEM FOR ANTI-DIABETIC DRUGS SELECTION BASED ON FUZZY REASONING AND ONTOLOGY TECHNIQUES." International Journal of Pattern Recognition and Artificial Intelligence 27, no. 04 (2013): 1359001. http://dx.doi.org/10.1142/s0218001413590015.

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Diabetes mellitus is a common chronic disease in recent years. According to the World Health Organization, the estimated number of diabetic patients will increase 56% in Asia from the year 2010 to 2025, where the number of anti-diabetic drugs that doctors are able to utilize also increase as the development of pharmaceutical drugs. In this paper, we present a recommendation system for anti-diabetic drugs selection based on fuzzy reasoning and ontology techniques, where fuzzy rules are used to represent knowledge to infer the usability of the classes of anti-diabetic drugs based on fuzzy reason

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39

ZHANG, GUOFENG, GUANRONG CHEN, TONGWEN CHEN, and MARÌA BELÉN D'AMICO. "DYNAMICAL ANALYSIS OF A NETWORKED CONTROL SYSTEM." International Journal of Bifurcation and Chaos 17, no. 01 (2007): 61–83. http://dx.doi.org/10.1142/s0218127407017173.

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A new network data transmission strategy was proposed in [Zhang & Chen, 2005], where the resulting nonlinear system was analyzed and the effectiveness of the transmission strategy was demonstrated via simulations. In this paper, we further generalize the results of Zhang and Chen [2005] in the following ways: (1) Construct first-return maps of the nonlinear systems formulated in [Zhang & Chen, 2005] and derive several existence conditions of periodic orbits and study their properties. (2) Formulate the new system as a hybrid system, which will ease the succeeding analysis. (3) Prove th

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40

ZHOU, TIANSHOU, YUN TANG, and GUANRONG CHEN. "CHEN'S ATTRACTOR EXISTS." International Journal of Bifurcation and Chaos 14, no. 09 (2004): 3167–77. http://dx.doi.org/10.1142/s0218127404011296.

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By applying the undetermined coefficient method, this paper finds homoclinic and heteroclinic orbits in the Chen system. It analytically demonstrates that the Chen system has one heteroclinic orbit of Ši'lnikov type that connects two nontrivial singular points. The Ši'lnikov criterion guarantees that the Chen system has Smale horseshoes and the horseshoe chaos. In addition, there also exists one homoclinic orbit joined to the origin. The uniform convergence of the series expansions of these two types of orbits are proved in this paper. It is shown that the heteroclinic and homoclinic orbits to

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41

Sprott, J. C. "New Chaotic Regimes in the Lorenz and Chen Systems." International Journal of Bifurcation and Chaos 25, no. 02 (2015): 1550033. http://dx.doi.org/10.1142/s0218127415500339.

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It has recently been shown that the Chen system with c > 0 is identical to the reversed-time Lorenz system with particular negative parameters and that the Chen system with c < 0 is identical to the forward-time Lorenz system with particular negative parameters. This note describes this new regime and shows that it admits chaotic solutions that were previously unexplored in either system.

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42

Lin, Meng-Lung, and Cheng-Wu Chen. "RETRACTED: Stability analysis of community and ecosystem hierarchies using the Lyapunov method." Journal of Vibration and Control 17, no. 13 (2010): 1930–37. http://dx.doi.org/10.1177/1077546310385737.

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In 2013 the Editor of Journal of Vibration and Control and SAGE became aware of a peer review ring involving assumed and fabricated identities that appeared to centre around Peter Chen at National Pingtung University of Education, Taiwan (NPUE). SAGE and the Editor then began a complex investigation into the case during the rest of 2013 and 2014. Following an unsatisfactory response from Peter Chen, NPUE was notified. NPUE were serious in addressing the Journal and SAGE’s concerns. NPUE confirmed that the institution was investigating Peter Chen. SAGE subsequently uncovered a citation ring inv

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Zhang, Fuchen, Xiaofeng Liao, Chunlai Mu, Guangyun Zhang, and Yi-An Chen. "On global boundedness of the Chen system." Discrete & Continuous Dynamical Systems - B 22, no. 4 (2017): 1673–81. http://dx.doi.org/10.3934/dcdsb.2017080.

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Lu, Xiaoting, Yongjian Liu, Aimin Liu, and Chunsheng Feng. "New geometric viewpoints to Chen chaotic system." Miskolc Mathematical Notes 23, no. 1 (2022): 339. http://dx.doi.org/10.18514/mmn.2022.3787.

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Fan, Tao, Chang-Zhong Chen, Xiao-Hong Ren, and Ping He. "Adaptive Synchronization of Delayed Chen Chaotic System." Interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity 3, no. 4 (2014): 367–78. http://dx.doi.org/10.5890/dnc.2014.12.001.

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Wang, Dong Xiao, and Bei Xing Mao. "Feedback Synchronization of Uncertain Chen Chaotic System." Advanced Materials Research 383-390 (November 2011): 4189–93. http://dx.doi.org/10.4028/www.scientific.net/amr.383-390.4189.

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In this paper, chaos synchronization is studied. Two schemes are proposed to synchronizing Chen chaotic system with all the system parameters unknown. Especially in the last two schemes, only one state variable is contained in the controller. Also, numerical simulations are given to illustrate the effectiveness of the methods.

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Alomari, A. K., M. S. M. Noorani, and R. Nazar. "Homotopy approach for the hyperchaotic Chen system." Physica Scripta 81, no. 4 (2010): 045005. http://dx.doi.org/10.1088/0031-8949/81/04/045005.

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Teiwes, Frederick C., and David M. Bachman. "Chen Yun and the Chinese Political System." Pacific Affairs 60, no. 4 (1987): 653. http://dx.doi.org/10.2307/2759191.

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DENG, XIJUN, and AIYONG CHEN. "INVARIANT ALGEBRAIC SURFACES OF THE CHEN SYSTEM." International Journal of Bifurcation and Chaos 21, no. 06 (2011): 1645–51. http://dx.doi.org/10.1142/s0218127411029331.

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In this paper, enlightened by the idea of the weight of a polynomial introduced by Swinnerton-Dyer [2002], we find all the invariant algebraic surfaces of the Chen system x′ = a(y - x), y′ = (c - a)x + cy - xz, z′ = xy - bz.

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Yassen, M. T. "Chaos control of Chen chaotic dynamical system." Chaos, Solitons & Fractals 15, no. 2 (2003): 271–83. http://dx.doi.org/10.1016/s0960-0779(01)00251-x.

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