Matrix and Inverse Matrix Projective Synchronization of Fractional-Order Time-Delay Chaotic Systems with Uncertainty

Abstract

In the present article, the matrix projective synchronization (MPS) and the inverse matrix projective synchronization (IMPS) have been analyzed with fractional-order chaotic systems with uncertain terms. First, we theoretically discussed both types of synchronizations. To achieve both types of synchronization, several required conditions are derived. We also drew portraits of Lyapunov’s exponents and bifurcation for more analysis. Furthermore, time-delay terms are also considered, giving an elegant application in real-world problems. Finally, numerical results agreed with the theoretical hypothesis. The numerical outcomes are shown through the graphical presentation.