Combination-combination synchronization of chaotic fractional order systems

Abstract

The quest for simple and practically implementable synchronization control functions is the fundamental motive for this research work because most of the control functions for synchronization are bulky thereby leading to complexity in implementation and high cost. This research paper examines the combination-combination synchronization of chaotic fractional order systems of identical order evolving from different initial conditions via the backstepping nonlinear control technique with the aim of reducing the control function’s complexity and cost. So, based on the stability theory of fractional order systems, stable synchronization are designed via a backstepping technique using chaotic fractional order Duffing and Aneodo as the paradigm. Numerical simulations are presented to confirm the feasibility of the analytical technique. The number of control functions has been sufficiently reduced compared to previous work hence reduction in control functions complexity and reduced cost of implementation. The outcome of this work may be useful to give a better understanding of the underlying dynamical behaviour among several interacting particles particularly in particle physics.