Diverse chimera and symmetry-breaking patterns induced by fractional derivation effect in a network of Stuart-Landau oscillators

Abstract

In this paper, we study the impact of fractional derivation on the symmetry-breaking dynamics of a network of coupled fractional-order Stuart-Landau oscillators. It is found that the value of the fractional derivatives order has a significant impact on the network dynamics. A decrease in the derivatives order results in complex dynamical patterns that are unobserved in the coupled integer-order system, namely solitary oscillation death state, multi-cluster chimera death, incoherent oscillation death, one-headed amplitude chimera, two-headed amplitude chimera, coherent travelling waves, and amplitude chimera on traveling waves background. It is also found that the fractional derivation can contribute to extend the lifetime of the amplitude chimeras. The stability of some of these states is investigated analytically, which allows to predict their regions of existence in the parameter space. Then, these dynamical features of the network are characterized to be mapped in the global parameter space. Significantly, with a decreasing derivatives order, the amplitude chimeras whose drifting oscillators are characterized by damped oscillations become short lived transient states that are eventually transformed into incoherent oscillation death states. A lower value of the fractional derivatives order inhibits amplitude chimeras and in-phase synchronized state, and promotes diverse oscillation death and chimera death states. The present study will deepen our understanding of chimera states in several natural systems that are essentially fractional in their dynamics.