Synchronization in counter-rotating oscillators
S.K.Bhowmick, Dibakar Ghosh, Syamal K. Dana
TL;DR
This paper introduces a general method to create counter-rotating oscillators, investigates their synchronization behavior, and provides analytical and experimental evidence of mixed synchronization phenomena.
Contribution
It presents a new rule for generating counter-rotating oscillators and analyzes their mixed synchronization stability both theoretically and experimentally.
Findings
Mixed synchronization can occur with coexisting complete and anti-synchronization.
Analytical stability conditions are derived for Rossler and Lorenz systems.
Experimental validation is provided using electronic circuits with chaotic and limit cycle oscillators.
Abstract
An oscillatory system can have clockwise and anticlockwise senses of rotation. We propose a general rule how to obtain counter-rotating oscillators from the definition of a dynamical system and then investigate synchronization. A type of mixed synchronization emerges in counter-rotating oscillators under diffusive scalar coupling when complete synchronization and antisynchronization coexist in different state variables. Stability conditions of mixed synchronization are obtained analytically in Rossler oscillator and Lorenz system. Experimental evidences of mixed synchronization are given for limit cycle as well as chaotic oscillators in electronic circuits.
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