| Abstract: | We present our study on the emergent states of two interacting nonlinear systems withdiffering dynamical time scales. We find that the inability of the interacting systems tofall in step leads to difference in phase as well as change in amplitude. If the mismatchis small, the systems settle to a frequency synchronized state with constant phasedifference. But as mismatch in time scale increases, the systems have to compromise to astate of no oscillations. We illustrate this for standard nonlinear systems and identifythe regions of quenched dynamics in the parameter plane. The transition curves to thisstate are studied analytically and confirmed by direct numerical simulations. As animportant special case, we revisit the well-known model of coupled ocean-atmosphere systemused in climate studies for the interactive dynamics of a fast oscillating atmosphere andslowly changing ocean. Our study in this context indicates occurrence of multi stableperiodic states and steady states of convection coexisting in the system, with a complexbasin structure. |
