Study Of the Stability Of Fractional Chaotic Systems With Sinusoidal Term

Abstract

In this memory, two typical chaotic maps with sine terms serve as the basis for studying the dynamics of two fractional-order chaotic maps. Using numerical methods including phase plots, bifurcation diagrams, Lyapunov exponents, and 0–1 test, the dynamic behavior of this map is examined. It is demonstrated that the suggested fractional maps display a variety of distinct dynamical behaviors, including coexisting attractors, with a change in fractional order. The charting of a bifurcation diagram for two symmetric beginning conditions illustrates the existence of coexistence attractors. Furthermore, three control strategies are presented. The suggested maps' states are stabilized, and their convergence to zero is guaranteed by the first two controllers. while the last synchronizes two non-identical fractional maps asymptotically. The conclusions are validated using numerical outcomes.