Fractional derivation stabilizing virtue-induced quenching phenomena in coupled oscillators

¹ Laboratory of Modeling and Simulation in Engineering, Biomimetics and Prototypes, Faculty of Science, University of Yaoundé I - PO Box 812, Yaoundé, Cameroon
² Fundamental Physics Laboratory, Department of Physics, Faculty of Science, University of Douala PO Box 24157, Douala, Cameroon

^(a) ngueut@yahoo.fr (corresponding author)

Received: 11 September 2015
Accepted: 2 November 2015

Abstract

We investigate quenching oscillations phenomena in a system of two diffusively and mutually coupled identical fractional-order Stuart-Landau oscillators. We first consider the uncoupled unit and find that the stabilizing virtue of the fractional derivative yields suppression of oscillations via a Hopf bifurcation. The oscillatory solutions of the fractional-order Stuart-Landau equation are provided as well. Quenching phenomena are then investigated in the coupled system. It is found that the fractional derivatives enhance oscillation death by widening its domain of existence in coupling strength space and initial conditions space, leading to oscillation death dominance. A region of stable homogeneous steady state appears where the uncoupled oscillators are resting and not oscillating as usually accepted for the realization of amplitude death.