Emergent rhythms in coupled nonlinear oscillators due to dynamic interactions.

The role of a new form of dynamic interaction is explored in a network of generic identical oscillators. The proposed design of dynamic coupling facilitates the onset of a plethora of asymptotic states including synchronous states, amplitude death states, oscillation death states, a mixed state (complete synchronized cluster and small amplitude desynchronized domain), and bistable states (coexistence of two attractors). The dynamical transitions from the oscillatory to the death state are characterized using an average temporal interaction approximation, which agrees with the numerical results in temporal interaction. A first-order phase transition behavior may change into a second-order transition in spatial dynamic interaction solely depending on the choice of initial conditions in the bistable regime. However, this possible abrupt first-order like transition is completely non-existent in the case of temporal dynamic interaction. Besides the study on periodic Stuart-Landau systems, we present results for the paradigmatic chaotic model of Rössler oscillators and the MacArthur ecological model.