Combination Synchronization of Three Different Fractional‐Order Delayed Chaotic Systems

Abstract

Time delay is a frequently encountered phenomenon in some practical engineering systems and introducing time delay into a system can enrich its dynamic characteristics. There has been a plenty of interesting results on fractional-order chaotic systems or integer-order delayed chaotic systems, but the problem of synchronization of fractional-order chaotic systems with time delays is in the primary stage. Combination synchronization of three different fractional-order delayed chaotic systems is investigated in this paper. It is an extension of combination synchronization of delayed chaotic systems or combination synchronization of fractional-order chaotic systems. With the help of stability theory of linear fractional-order systems with multiple time delays, we design controllers to achieve combination synchronization of three different fractional-order delayed chaotic systems. In addition, numerical simulations have been performed to demonstrate and verify the theoretical analysis.

Dynamical analysis and triple compound combination anti-synchronization of novel fractional chaotic system

“…In this regard, the lesser time it takes to synchronize, the better is the synchronization method. In Li et al (2019) Bo et al performed combination synchronization at 3 units of time. Meanwhile, Sun et al (2014) achieved the compound synchronization at 5 units.…”

Projection Synchronization of a Class of Complex Chaotic Systems with Both Uncertainty and Disturbance

“…ey achieved chaotic synchronization of two identical systems with different initial conditions in electronic experiments. Until now, many types of chaotic synchronization have been discovered, such as complete synchronization, phase synchronization, lag synchronization, antisynchronization, and projection synchronization, and many other important results have been obtained (see references [2][3][4][5][6][7][8]). Especially, projective synchronization has received much attention due to its faster communication and proportionality between the dynamical systems.…”