Dual Compound–Compound Synchronization of Twelve n-Dimensional Dynamical Systems

A dual synchronization scheme combined with compound–compound synchronization is proposed. In usual compound–compound synchronization scheme, synchronization has been achieved for six dynamical systems, while in the presented scheme compound–compound synchronization has been developed in the dual synchronization frame involving twelve dynamical systems. Numerous synchronization schemes such as dual compound, dual combination, compound–compound and compound synchronization may be derived as particular cases of the presented scheme. By employing nonlinear control method and Lyapunov stability criteria, controllers are designed. Illustrations are presented using Genesio-Tesi and Wang chaotic systems. Computational results are presented to show the effectiveness of the proposed methodology. A good agreement has been obtained between analytical methodology and numerical treatment.

[1]  Ayub Khan,et al.  Multiswitching compound–compound synchronisation of six chaotic systems , 2018, Pramana.

[2]  Xing-yuan Wang,et al.  Dynamic analysis of the fractional-order Liu system and its synchronization. , 2007, Chaos.

[3]  E. M. Shahverdiev,et al.  Lag synchronization in time-delayed systems , 2002 .

[4]  Saad Fawzi AL-Azzawi,et al.  Anti-synchronization of nonlinear dynamical systems based on Gardano's method , 2017 .

[5]  Hamed Tirandaz.  On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method , 2017 .

[6]  Hongyue Du,et al.  Function projective synchronization in coupled chaotic systems , 2010 .

[7]  K. S. Ojo,et al.  Generalized reduced-order hybrid combination synchronization of three Josephson junctions via backstepping technique , 2014 .

[8]  Compound synchronization of fourth-order memristor oscillator , 2014 .

[9]  Hao Zhang,et al.  Topology Identification and Module–Phase Synchronization of Neural Network With Time Delay , 2017, IEEE Transactions on Systems, Man, and Cybernetics: Systems.

[10]  A. Almatroud Othman,et al.  Adaptive dual anti-synchronization of chaotic systems with fully uncertain parameters , 2016 .

[11]  Jiang-Wen Xiao,et al.  Impulsive control for synchronization of a class of continuous systems. , 2004, Chaos.

[12]  P. Davis,et al.  Dual synchronization of chaos , 2000 .

[13]  Muhammad Shafiq,et al.  Globally exponential multi switching-combination synchronization control of chaotic systems for secure communications , 2018, Chinese Journal of Physics.

[14]  Ayub Khan,et al.  Dual combination combination multi switching synchronization of eight chaotic systems , 2017, ArXiv.

[15]  Guangzhao Cui,et al.  Combination–combination synchronization among four identical or different chaotic systems , 2013 .

[16]  Feiqi Deng,et al.  Double-compound synchronization of six memristor-based Lorenz systems , 2014 .

[17]  Huaguang Zhang,et al.  Networked Synchronization Control of Coupled Dynamic Networks With Time-Varying Delay , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[18]  Xiaomei Yan,et al.  Modified projective synchronization of fractional-order chaotic systems based on active sliding mode control , 2013, 2013 25th Chinese Control and Decision Conference (CCDC).

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

[20]  M. Noorani,et al.  On anti-synchronization of chaotic systems via nonlinear control , 2009 .

[21]  S. M. Lee,et al.  Adaptive synchronization of Genesio-Tesi chaotic system via a novel feedback control , 2007 .

[22]  Yi Shen,et al.  Compound-combination synchronization of five chaotic systems via nonlinear control , 2016 .

[23]  Luo Runzi,et al.  Combination synchronization of three classic chaotic systems using active backstepping design. , 2011, Chaos.

[24]  Luo Runzi,et al.  Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication. , 2012, Chaos.

[25]  Jun Ma,et al.  Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system , 2011 .

[26]  Xing-yuan Wang,et al.  Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control , 2009 .

[27]  Jiang Suxia,et al.  Dual Combination Synchronization of Six Chaotic Systems , 2016 .

[28]  Guanrong Chen,et al.  Pinning control and synchronization on complex dynamical networks , 2014, International Journal of Control, Automation and Systems.

[29]  Chi-Ching Yang,et al.  Adaptive terminal sliding mode control subject to input nonlinearity for synchronization of chaotic gyros , 2013, Commun. Nonlinear Sci. Numer. Simul..

[30]  Yi Shen,et al.  Compound synchronization of four memristor chaotic oscillator systems and secure communication. , 2013, Chaos.

[31]  Xing-yuan Wang,et al.  Projective synchronization of fractional order chaotic system based on linear separation , 2008 .

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

[33]  Xingyuan Wang,et al.  Chaos in the fractional-order complex Lorenz system and its synchronization , 2013 .

[34]  A. Almatroud Othman,et al.  Adaptive dual synchronization of chaotic and hyperchaotic systems with fully uncertain parameters , 2016 .

[35]  Da Lin,et al.  Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation , 2010, Fuzzy Sets Syst..

[36]  Xiangjun Wu,et al.  Generalized projective synchronization of the fractional-order Chen hyperchaotic system , 2009 .

[37]  Mayank Srivastava,et al.  Triple Compound Synchronization Among Eight Chaotic Systems with External Disturbances via Nonlinear Approach , 2019, Differential Equations and Dynamical Systems.

[38]  Lin Wang,et al.  3-scroll and 4-scroll chaotic attractors generated from a new 3-D quadratic autonomous system , 2009 .