Combination-Difference Synchronization of Fractional Order Chaotic Duffing Oscillator and Financial Systems With Parameter Mismatch

Abstract

This research work is born out of the desire to design an effective synchronization scheme that could give a better understanding of the coordination of multiple processes and effective communication among various components of a complex system or between different groups of complex systems As a result, this research work presents combination-difference synchronization of fractional order chaotic (FOC) systems with parameter mismatches evolving from different initial conditions. Using the FOC Duffing oscillators and FOC financial systems as a paradigm, the backstepping technique is applied to design control laws for the achievement of combination-difference synchronization. These control laws enable the differences between the sums of the variables of the drive systems and differences of the variables of the response systems to converge to zero which confirms the achievement of combination difference synchronization. Numerical simulations provided confirm the effectiveness of the combination-difference synchronization technique. This result could be used to explain different interactions among particles and neurons of the same or different dynamical behaviour