Period-doubling route from synchronization to chaos of an oscillator coupled to a regular oscillator

TL;DR

This paper investigates how increasing coupling strength in an oscillator array leads from synchronization to chaos via period doubling, revealing complex transitions in collective dynamics.

Contribution

It introduces a novel coupling scheme where oscillators are driven through an activator to a regular oscillator, uncovering new routes to chaos and order.

Findings

Weak coupling results in independent oscillators.

Increasing coupling causes a transition to synchronization.

Further coupling induces period doubling and chaos.

Abstract

Spatiotemporal chaos in the form of defect-mediated turbulence is known for oscillators coupled by diffusion. Here we explore the same conditions that produce defect turbulence, in an array of oscillators that are coupled through the activator to a regular oscillator. We find that for very small coupling the oscillators behave independent of each other and then there is a transition to complete synchronization. On further increasing the coupling strength, there is period doubling and a transition to chaotic behavior of each driven unit. However the global behavior shows some ordering, and the period-two oscillations become period-one with a further increase in the coupling strength.