Suppression of dynamics and frequency synchronization in coupled slow and fast dynamical systems

TL;DR

This paper investigates how differing time scales in coupled nonlinear systems affect their synchronization and dynamics, revealing transitions from frequency locking to quenched states and complex multistability, with implications for climate models.

Contribution

It provides a detailed analysis of the suppression of oscillations and synchronization in coupled systems with different time scales, including analytical and numerical results, and revisits climate models for multistability.

Findings

Small mismatch leads to frequency synchronization with constant phase difference.

Large mismatch causes systems to settle into no-oscillation states.

Reveals multistability and complex basin structures in climate-related models.

Abstract

We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in amplitude. If the mismatch is small, the systems settle to a frequency synchronized state with constant phase difference. But as mismatch in time scale increases, the systems have to compromise to a state of no oscillations. We illustrate this for standard nonlinear systems and identify the regions of quenched dynamics in the parameter plane. The transition curves to this state are studied analytically and confirmed by direct numerical simulations. As an important special case, we revisit the well-known model of coupled ocean atmosphere system used in climate studies for the interactive dynamics of a fast oscillating atmosphere and slowly changing ocean. Our study in this context indicates occurrence of multi stable periodic states and steady states of convection coexisting in the system, with a complex basin structure.