Effects of periodically modulated coupling on amplitude death in nonidentical oscillators

Abstract

The effects of periodically modulated coupling on amplitude death (AD) in two coupled nonidentical oscillators are explored. The AD domain is significantly influenced by tuning the modulation amplitude and frequency of the coupling. There is an optimal value of the modulation amplitude of the coupling with which the largest AD domain is observed in the parameter spaces. The AD domain is enlarged (shrunk) with the decrease of the modulation frequency for a given small (large) modulation amplitude. The mechanism of AD in the presence of periodic modulation in the coupling is investigated based on the local conditional Lyapunov exponent. The stability of the AD state can be availably characterized by the conditional Lyapunov exponents of the coupled system. The transition process from oscillating to the AD state is clearly verified by the fact that the conditional Lyapunov exponent transits from positive to negative. Our results are helpful to many potential applications in neuroscience and dynamical control in engineering.