Mixed mode oscillation suppression states in coupled oscillators

Abstract

We report a new collective dynamical state, namely the {\it mixed mode oscillation suppression} state where different set of variables of a system of coupled oscillators show different types of oscillation suppression states. We identify two variants of it: The first one is a {\it mixed mode death} (MMD) state where a set of variables of a system of coupled oscillators show an oscillation death (OD) state, while the rest are in an amplitude death (AD) state under the identical parametric condition. In the second mixed death state (we refer it as the MNAD state) a nontrivial bistable AD and a monostable AD state appear simultaneously to different set of variables of a same system. We find these states in paradigmatic chaotic Lorenz system and Lorenz-like system under generic coupling schemes. We identify that while the reflection symmetry breaking is responsible for the MNAD state, the breaking of both the reflection and translational symmetries result in the MMD state. Using a rigorous bifurcation analysis we establish the occurrence of the MMD and MNAD states, and map their transition routes in parameter space. Moreover, we report the {\it first} experimental observation of the MMD and MNAD states that supports our theoretical results. We believe that this study will broaden our understanding of oscillation suppression states, subsequently, it may have applications in many real physical systems, such as laser and geomagnetic systems, whose mathematical models mimic the Lorenz system.