The mechanism of switching combination synchronization for three distinct nonautonomous systems under sinusoidal constraints

In this paper, the mechanism of switching combination synchronization the controlled Duffing oscillator with Van der Pol system and Pendulum system is studied. Based on the theory of discontinuous dynamical systems, the analytical conditions for chaos synchronization of three different systems are obtained under sinusoidal constraints. With these conditions, the control parameter maps and the synchronization invariant sets are derived, respectively. Numerical illustrations for partial and full combination synchronization among three systems are carried out. The circuits of switching synchronization are used for the validation of the numerical simulations.

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

[2]  Saleh Mobayen,et al.  Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control. , 2018, ISA transactions.

[3]  Mohammad Hadi Farahi,et al.  Synchronization of Multiple Chaotic Systems using a nonlinear Grouping feedback function method , 2018, Mechatron. Syst. Control..

[4]  Viet-Thanh Pham,et al.  Coexistence of generalized synchronization and inverse generalized synchronization between chaotic and hyperchaotic systems , 2018, Nonlinear Analysis: Modelling and Control.

[5]  A. Luo.  Regularity and Complexity in Dynamical Systems , 2011 .

[6]  Vijay K. Yadav,et al.  Dual combination synchronization of the fractional order complex chaotic systems , 2017 .

[7]  Binoy Krishna Roy,et al.  Memristor-based novel complex-valued chaotic system and its projective synchronisation using nonlinear active control technique , 2019 .

[8]  Ayub Khan,et al.  Multiswitching dual combination synchronization of time‐delay chaotic systems , 2018, Mathematical Methods in the Applied Sciences.

[9]  Sonia Hammami.  Multi-switching combination synchronization of discrete-time hyperchaotic systems for encrypted audio communication , 2019, IMA J. Math. Control. Inf..

[10]  A. Luo,et al.  On parameter characteristics of chaotic synchronization in two nonlinear gyroscope systems , 2012 .

[11]  Uchechukwu E. Vincent,et al.  Multi-switching combination synchronization of chaotic systems , 2015, Nonlinear Dynamics.

[12]  Muzaffar Ahmad Bhat,et al.  Multi‐switching combination–combination synchronization of non‐identical fractional‐order chaotic systems , 2017 .

[13]  Yun Wang,et al.  Combination Synchronization of Three Different Fractional-Order Delayed Chaotic Systems , 2019, Complex..

[14]  Hamed Tirandaz,et al.  Chaos synchronization and parameter identification of a finance chaotic system with unknown parameters, a linear feedback controller , 2018, Alexandria Engineering Journal.

[15]  Jun Zhang,et al.  Multi-switching combination synchronization of spatiotemporal coupled chaotic systems with complexities , 2019 .

[16]  Mohamad Rushdan Md. Said,et al.  GENERALIZED PROJECTIVE SERIES SYNCHRONIZATION BETWEEN CHAOTIC SYSTEMS AND ITS APPLICATION , 2018 .

[17]  Qian Ye,et al.  Adaptive Feedback Control for Synchronization of Chaotic Neural Systems with Parameter Mismatches , 2018, Complex..

[18]  Tene Alain Giresse,et al.  Chaos generalized synchronization of coupled Mathieu-Van der Pol and coupled Duffing-Van der Pol systems using fractional order-derivative , 2017 .

[19]  Min Zhang,et al.  Cascading failure in multilayer network with asymmetric dependence group , 2019, International Journal of Modern Physics C.

[20]  Xiao-Qing Zhang,et al.  Dual projective synchronization between integer-order and fractional-order chaotic systems , 2017 .

[21]  Fuhong Min,et al.  Analysis of generalized projective synchronization for a chaotic gyroscope with a periodic gyroscope , 2012 .

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

[23]  Albert C. J. Luo,et al.  A theory for synchronization of dynamical systems , 2009 .

[24]  Ming-Feng Ge,et al.  Finite-time synchronization of memristor chaotic systems and its application in image encryption , 2019, Appl. Math. Comput..

[25]  Zhengze Wu,et al.  Generalized Chaos Synchronization Circuit Simulation and Asymmetric Image Encryption , 2019, IEEE Access.

[26]  Haifei Liu,et al.  Credit Risk Contagion in an Evolving Network Model Integrating Spillover Effects and Behavioral Interventions , 2018, Complex..

[27]  Ana Dalia Pano-Azucena,et al.  Arduino-based chaotic secure communication system using multi-directional multi-scroll chaotic oscillators , 2016, Nonlinear Dynamics.

[28]  C. Anteneodo,et al.  Complete synchronization of chaotic maps under advection , 2018 .

[29]  Muzaffar Ahmad Bhat,et al.  Complete synchronisation of non-identical fractional order hyperchaotic systems using active control , 2019 .

[30]  Albert C. J. Luo,et al.  A theory for flow switchability in discontinuous dynamical systems , 2008 .

[31]  Viet-Thanh Pham,et al.  An adaptive observer synchronization using chaotic time-delay system for secure communication , 2017, Nonlinear Dynamics.

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

[33]  Albert C. J. Luo,et al.  Complex Dynamics of Projective Synchronization of Chua Circuits with Different Scrolls , 2015, Int. J. Bifurc. Chaos.