Dual Combination Synchronization of the Fractional Order Complex Chaotic Systems

Abstract

In this article, the authors have proposed a novel scheme for the dual combination synchronization among four master systems and two slave systems for the fractional order complex chaotic systems. Dual combination synchronization for the integer order has already been investigated in real space; but for the case of fractional order in complex space, it is the first of its kind. Due to complexity and presence of additional variable, it will be more secure and interesting to transmit and receive signals in communication theory. Based on the Lyapunov stability theory, six complex chaotic systems are considered and corresponding controllers are designed to achieve synchronization. The special cases, such as combination synchronization, projective synchronization, complete synchronization, and many more, can be derived from the proposed scheme. The corresponding theoretical analysis and numerical simulations are shown to verify the feasibility and effectiveness of the proposed dual combination synchronization scheme.

Multiswitching dual combination synchronization of time‐delay chaotic systems

“…In this case, matrices P 1 , P 2 are chosen as identity matrices and Q 1 , Q 2 , R 1 , R 2 are taken as diag( − 1, − 1, − 1), which lead to antisynchronization. Hence, the initial conditions for the errors ( (131) E 11 , (213) E 21 , (322) E 31 ) and ( (123) E 12 , (212) E 22 , (331) E 32 ) are (2.7, 4, 6) and (12,11,13), respectively. Figures 8 and (9) show antisynchronization for (x 11 , (y 31 + z 11 )) and (x 21 , (y 11 + z 31 )), respectively.…”

“…[7][8][9] Dual synchronization was first investigated by Liu and Davis. 10 As a significant development, dual combination synchronization 11,12 has been developed for multidrive and response systems.…”

A New Type of Combination Synchronization among Multiple Chaotic Systems

“…Sun et al launched investigations on the finite-time combination synchronization of complex-variable chaotic systems with unknown parameters via sliding mode control [28,29]. Singh et al proposed a novel scheme for the dual combination synchronization among four master systems and two slave systems for the fractional-order complex chaotic systems with stability analysis [30].…”

Dual combination combination multi switching synchronization of eight chaotic systems

“…In all prior work the common theme is to consider one pair of drive system with one pair of response system. Only recently the idea of dual synchronization was extended to two pair of drive systems and one pair of response system [18,19].…”