Synchronization in coupled integer and fractional-order maps

Coupled differential equations and coupled maps have been used to model numerous systems in science and engineering. The role of memory in these systems is modelled using fractional calculus. However, different parts of the system may respond to memory in a different manner. We study coupled system in which an integer order system is coupled to a fractional order alpha system bidirectionally or unidirectionally for various values of alpha. It is possible to analytically determine the stability of the fixed point for a unidirectionally coupled linear system. It is found to depend on the stability of the fractional system. The stability criterion extends to the nonlinear case as well. If we linearize the nonlinear map around the fixed point, the criterion for the linear case also holds for the stability of the fixed point of coupled nonlinear maps. (C) 2022 Elsevier Ltd. All rights reserved.

Automated summary

Coupled differential equations and coupled maps are widely used in science and engineering. This study investigates the coupling between integer order systems and fractional order systems, and reveals the dependence of stability on the stability of the fractional system, providing stability criteria.