Synchronization Between a Class of Variable-Order Fractional Hyperjerk Chaotic Systems

Resumen

Variable-order fractional derivatives can be considered as a natural and analytical extension of constant fractional-order derivatives. In variable-order derivatives, the order can vary continuously as a function of either dependent or independent variables of differentiation, such as time, space, or even independent external variables. The main contribution of this paper is the use of fractional orders that vary in time for a new class of chaotic systems. This paper also studies the synchronization between a new class of variable-order fractional hyperjerk chaotic systems. The Grunwald-Letnikov’s definition of fractional derivative is ¨ implemented to solve variable-order fractional problems. In addition, considering the bifurcation diagram, a periodic function was proposed to vary the order of the derivative. The chaos synchronization will be carried out via an active control approach. Regarding the results and focusing on synchronization, it can be observed that the error converges asymptotically to zero. Finally, the theoretical work agrees satisfactorily with the numerical results.