Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen-Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchronization, we use the well-known PID (Proportional-Integral-Derivative) control theory and the Lyapunov-Krasovskii stability theory for discrete systems of a variable fractional order. We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.

Automated summary

In this research paper, the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations is solved using PID control theory and Lyapunov-Krasovskii stability theory. The results obtained through simulation with examples demonstrate satisfactory outcomes in achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay.