Analysis, Control, and Synchronization of a 3-D Novel Jerk Chaotic System with Two Quadratic Nonlinearities

In this research work, a seven-term 3-D novel jerk chaotic system with two quadratic nonlinearities has been proposed. The basic qualitative properties of the novel jerk chaotic system have been described in detail. Next, an adaptive backstepping controller is designed to stabilize the novel jerk chaotic system with two unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve complete chaos synchronization of the identical novel jerk chaotic systems with two unknown parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed for the 3-D novel jerk chaotic system.

[1]  Jiye Zhang,et al.  Synchronizing chaotic systems using backstepping design , 2003 .

[2]  Lee,et al.  Competition between magnetism and superconductivity in rare-earth nickel boride carbides. , 1994, Physical review. B, Condensed matter.

[3]  Sundarapandian Vaidyanathan,et al.  Generalized projective synchronization of Elhadj chaotic systems via adaptive control , 2013, 2013 International Conference on Green Computing, Communication and Conservation of Energy (ICGCE).

[4]  Sundarapandian Vaidyanathan,et al.  ADAPTIVE CONTROL AND SYNCHRONIZATION OF THE CAI SYSTEM , 2012 .

[5]  Guanrong Chen,et al.  YET ANOTHER CHAOTIC ATTRACTOR , 1999 .

[6]  Sundarapandian Vaidyanathan.  Analysis, control and synchronisation of a six-term novel chaotic system with three quadratic nonlinearities , 2014, Int. J. Model. Identif. Control..

[7]  Sundarapandian Vaidyanathan,et al.  ADAPTIVE BACKSTEPPING CONTROLLER AND SYNCHRONIZER DESIGN FOR ARNEODO CHAOTIC SYSTEM WITH UNKNOWN PARAMETERS , 2012 .

[8]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[9]  Robert M. May,et al.  Limit Cycles in Predator-Prey Communities , 1972, Science.

[10]  Uchechukwu E. Vincent,et al.  Synchronization of chaos in non-identical parametrically excited systems , 2009 .

[11]  Guoliang Cai,et al.  Adaptive Backstepping Control of the Uncertain Unified Chaotic System , 2007 .

[12]  J. Sprott.  Chaos and time-series analysis , 2001 .

[13]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[14]  Tomasz Kapitaniak,et al.  Controlling Chaos: Theoretical and Practical Methods in Non-linear Dynamics , 1996 .

[15]  V. Sundarapandian,et al.  Global Chaos Synchronization of Hyperchaotic Lorenz and Hyperchaotic Chen Systems by Adaptive Control , 2011 .

[16]  J. C. Sprotta.  Some simple chaotic jerk functions , 1997 .

[17]  M. Lakshmanan,et al.  Chaos in Nonlinear Oscillators: Controlling and Synchronization , 1996 .

[18]  Chongxin Liu,et al.  A new chaotic attractor , 2004 .

[19]  V. Sundarapandian,et al.  Analysis, control, synchronization, and circuit design of a novel chaotic system , 2012, Math. Comput. Model..

[20]  V. Sundarapan,et al.  Anti-Synchronization of Lu and Pan Chaotic Systems by Adaptive Nonlinear Control , 2011 .

[21]  V. Sundarapan,et al.  Adaptive Anti-Synchronization of Uncertain Tigan and Li Systems , 2012 .

[22]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of Hyperchaotic Pang and Hyperchaotic Wang Systems via Adaptive Control , 2011 .

[23]  Yi Feng,et al.  COMPUTATIONAL ANALYSIS OF CODE COLLABORATION PATTERN AND SEMANTIC ROLE , 2012 .

[24]  Sundarapandian Vaidyanathan,et al.  Generalized Projective Synchronization of Three-Scroll Chaotic Systems via Active Control , 2012 .

[25]  J. Kurths,et al.  From Phase to Lag Synchronization in Coupled Chaotic Oscillators , 1997 .

[26]  Viet-Thanh Pham,et al.  Constructing a Novel No-Equilibrium Chaotic System , 2014, Int. J. Bifurc. Chaos.

[27]  Guoliang Cai,et al.  Chaos Synchronization of a New Chaotic System via Nonlinear Control , 2007 .

[28]  Ming-Chang Pai,et al.  Global synchronization of uncertain chaotic systems via discrete-time sliding mode control , 2014, Appl. Math. Comput..

[29]  M. Feigenbaum.  Universal behavior in nonlinear systems , 1983 .

[30]  V. Sundarapan,et al.  Hybrid Synchronization of Hyperchaotic Lorenz and Hyperchaotic Chen Systems via Active Control , 2012 .

[31]  O. Rössler.  An equation for continuous chaos , 1976 .

[32]  V. Sundarapan,et al.  Sliding Controller Design of Hybrid Synchronization of Four-Wing Chaotic Systems , 2011 .

[33]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of Hyperchaotic Wang-Chen and Hyperchaotic Lorenz Systems by Active Non-linear Control , 2011 .

[34]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of n-Scroll Chua Circuit and Lur’e System using Backstepping Control Design with Recursive Feedback , 2014 .

[35]  Sundarapandian Vaidyanathan,et al.  Analysis, synchronization and circuit design of a novel butterfly attractor , 2014 .

[36]  F. Takens,et al.  On the nature of turbulence , 1971 .

[37]  Alain Arneodo,et al.  Possible new strange attractors with spiral structure , 1981 .

[38]  M. Yassen.  Controlling, synchronization and tracking chaotic Liu system using active backstepping design , 2007 .

[39]  Uchechukwu E. Vincent,et al.  Synchronization of identical and non-identical 4-D chaotic systems using active control , 2008 .

[40]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  S. Vaidyanathan.  Analysis and Adaptive Synchronization of Two Novel Chaotic Systems with Hyperboli c Sinusoidal and Cosinusoidal Nonlinearity and Unknown Parameters , 2013 .

[42]  H. Fujisaka,et al.  Stability Theory of Synchronized Motion in Coupled-Oscillator Systems , 1983 .

[43]  Marion Kee,et al.  Analysis , 2004, Machine Translation.

[44]  Julien Clinton Sprott,et al.  A new class of chaotic circuit , 2000 .

[45]  Sundarapandian Vaidyanathan,et al.  Adaptive backstepping control, synchronization and circuit simulation of a 3-D novel jerk chaotic system with two hyperbolic sinusoidal nonlinearities , 2014 .

[46]  Sr Technical,et al.  Anti-synchronization of Four-wing Chaotic Systems via Sliding Mode Control , 2012 .

[47]  An elegant chaos. , 2014, Nature.

[48]  V. Sundarapandian,et al.  Analysis and Anti-Synchronization of a Novel Chaotic System via Active and Adaptive Controllers , 2013 .

[49]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[50]  J. Sprott,et al.  Some simple chaotic flows. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[51]  Julien Clinton Sprott,et al.  Simple chaotic flows with a line equilibrium , 2013 .

[52]  Fanyu Meng,et al.  Pinning synchronization of the drive and response dynamical networks with lag , 2014, Archives of Control Sciences.

[53]  Dequan Li,et al.  A three-scroll chaotic attractor , 2008 .

[54]  Sundarapandian Vaidyanathan,et al.  Analysis and adaptive synchronization of eight-term 3-D polynomial chaotic systems with three quadratic nonlinearities , 2014 .

[55]  Rajagopal Karthikeyan,et al.  Hybrid Chaos Synchronization of Four–Scroll Systems via Active Control , 2014 .

[56]  Sundarapandian Vaidyanathan.  Global chaos synchronisation of identical Li-Wu chaotic systems via sliding mode control , 2014, Int. J. Model. Identif. Control..

[57]  P. Sarasu,et al.  The Generalized Projective Synchronization of Hyperchaotic Lorenz and Hyperchaotic Qi Systems via Active Control , 2011 .

[58]  H. Agiza,et al.  Synchronization of Rossler and Chen chaotic dynamical systems using active control , 2001, Physics Letters A.

[59]  Sundarapandian Vaidyanathan,et al.  Global Chaos Synchronization of WINDMI and Coullet Chaotic Systems using Adaptive Backstepping Control Design , 2014 .

[60]  Ronnie Mainieri,et al.  Projective Synchronization In Three-Dimensional Chaotic Systems , 1999 .

[61]  Jian Xu,et al.  Projective synchronization of different chaotic time-delayed neural networks based on integral sliding mode controller , 2010, Appl. Math. Comput..

[62]  J. Yorke,et al.  Chaos: An Introduction to Dynamical Systems , 1997 .

[63]  Sundarapandian Vaidyanathan,et al.  Hybrid Synchronization of n-scroll Chaotic Chua Circuits using Adaptive Backstepping Control Design with Recursive Feedback , 2013 .

[64]  Vadim S. Anishchenko,et al.  Antiphase Synchronization in symmetrically Coupled Self-oscillators , 2000, Int. J. Bifurc. Chaos.

[65]  Gregory L. Baker,et al.  Chaotic Dynamics: An Introduction , 1990 .

[66]  Jinhu Lu,et al.  A New Chaotic Attractor Coined , 2002, Int. J. Bifurc. Chaos.

[67]  Jinsong Chen.  Mechanical Properties of Electrolyte Jet Electrodeposited Nickel Foam , 2013 .