Chaos Control and Synchronization of a Complex Rikitake Dynamo Model

A novel chaotic system called complex Rikitake system is proposed. Dynamical properties, including symmetry, dissipation, stability of equilibria, Lyapunov exponents and bifurcation, are analyzed on the basis of theoretical analysis and numerical simulation. Further, based on feedback control method, the complex Rikitake system can be controlled to any equilibrium points. Additionally, this paper not only proves the existence of two types of synchronization schemes in the complex Rikitake system but also designs adaptive controllers to realize them. The proposed results are verified by numerical simulations.

[1]  Emad E. Mahmoud,et al.  Complex lag synchronization of two identical chaotic complex nonlinear systems , 2014 .

[2]  Rongwei Guo,et al.  Projective synchronization of a class of chaotic systems by dynamic feedback control method , 2017 .

[3]  Guangzhao Cui,et al.  Combination complex synchronization of three chaotic complex systems , 2015 .

[4]  Zhouchao Wei,et al.  Dynamics and delayed feedback control for a 3D jerk system with hidden attractor , 2015 .

[5]  G. Mahmoud,et al.  Lag synchronization of hyperchaotic complex nonlinear systems , 2012 .

[6]  Edward Ott,et al.  Controlling chaos , 2006, Scholarpedia.

[7]  Kehui Sun,et al.  Multivariate permutation entropy and its application for complexity analysis of chaotic systems , 2016 .

[8]  Ping Liu,et al.  Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters , 2011 .

[9]  Jian Liu,et al.  The characteristics and self-time-delay synchronization of two-time-delay complex Lorenz system , 2019, J. Frankl. Inst..

[10]  Keisuke Ito,et al.  Chaos in the Rikitake two-disc dynamo system , 1980 .

[11]  Vladimir L. Derbov,et al.  Complex Lorenz equations , 1997, Other Conferences.

[12]  Fangfang Zhang,et al.  Complex function projective synchronization of complex chaotic system and its applications in secure communication , 2013, Nonlinear Dynamics.

[13]  Jian Chu,et al.  Control Chaos for Permanent Magnet Synchronous Motor Base on Adaptive Backstepping of Error Compensation , 2016 .

[14]  Guanrong Chen,et al.  On feedback control of chaotic continuous-time systems , 1993 .

[15]  Chun-Lai Li,et al.  Dynamics and Synchronization of a Memristor-Based Chaotic System with No Equilibrium , 2019, Complex..

[16]  T. Rikitake,et al.  Oscillations of a system of disk dynamos , 1958, Mathematical Proceedings of the Cambridge Philosophical Society.

[17]  Rongwei Guo,et al.  Hybrid Synchronization Problem of a Class of Chaotic Systems by an Universal Control Method , 2018, Symmetry.

[18]  Karthikeyan Rajagopal,et al.  FPGA implementation of adaptive sliding mode control and genetically optimized PID control for fractional-order induction motor system with uncertain load , 2017 .

[19]  Tassos Bountis,et al.  Active Control and Global Synchronization of the Complex Chen and lÜ Systems , 2007, Int. J. Bifurc. Chaos.

[20]  Rongwei Guo.  A simple adaptive controller for chaos and hyperchaos synchronization , 2008 .

[21]  Emad E. Mahmoud,et al.  Complex complete synchronization of two nonidentical hyperchaotic complex nonlinear systems , 2014 .

[22]  Cuimei Jiang,et al.  Generalized combination complex synchronization of new hyperchaotic complex Lü-like systems , 2015, Advances in Difference Equations.

[23]  Xiaobing Zhou,et al.  Combination Synchronization of Three Identical or Different Nonlinear Complex Hyperchaotic Systems , 2013, Entropy.

[24]  Mehdi Roopaei,et al.  Review article on adaptive synchronization of chaotic systems with unknown parameters , 2011 .

[25]  Hongjun Liu,et al.  Image encryption using complex hyper chaotic system by injecting impulse into parameters , 2019, Appl. Math. Comput..

[26]  Emad E. Mahmoud,et al.  Complete synchronization of chaotic complex nonlinear systems with uncertain parameters , 2010 .

[27]  Emad E. Mahmoud,et al.  A New Nonlinear Chaotic Complex Model and Its Complex Antilag Synchronization , 2017, Complex..

[28]  J. Yorke,et al.  The liapunov dimension of strange attractors , 1983 .

[29]  Emad E. Mahmoud,et al.  Dynamical properties and complex anti synchronization with applications to secure communications for a novel chaotic complex nonlinear model , 2018 .

[30]  S. Vaidyanathan,et al.  Dynamical Analysis and FPGA Implementation of a Novel Hyperchaotic System and Its Synchronization Using Adaptive Sliding Mode Control and Genetically Optimized PID Control , 2017 .

[31]  Louis M Pecora,et al.  Synchronization of chaotic systems. , 2015, Chaos.

[32]  Binoy Krishna Roy,et al.  Hidden attractors in a new complex generalised Lorenz hyperchaotic system, its synchronisation using adaptive contraction theory, circuit validation and application , 2018 .

[33]  Akbar Zada,et al.  Synchronization of bidirectional N-coupled fractional-order chaotic systems with ring connection based on antisymmetric structure , 2019, Advances in Difference Equations.