Turing instability in nonlinear chemical oscillators coupled via an active medium

•Spontaneous differentiation in strongly coupled non-linear chemical oscillators via Turing instability.•Fundamental role of the external active medium in synchronization of non-linear chemical oscillators.•Cross-diffusion in synchronization mechanism.•Network description of non-linear chemical oscillators coupled via an active external medium. Nonlinear chemical oscillators have attracted a great deal of interest in the scientific community due to the wide range of non-trivial behaviors they exhibit and also due to their ability to reproduce behaviors found in nature. We consider this system and mathematically propose a different description based on a network-type topology. Within this context, we demonstrate the existence of a new type of behavior, induced by a Turing instability, characterized by the existence of two sets of chemical oscillators with different properties. The parameters of the model are analyzed and the influence on the collective behavior described.