We describe a simple model mimicking diffusively coupled chemical micro-oscillators. We characterize the rich variety of dynamical states emerging from the model under variation of time delay in coupling, coupling strength and boundary conditions. The spatiotemporal patterns obtained include clustering, mixed dynamics, inhomogeneous steady states and amplitude death. Further, under delay in coupling, the model yields transitions from phase to antiphase oscillations, reminiscent of that observed in experiments [M Toiya et al, J. Chem. Lett. 1, 1241 (2010)].

We study the role of mean-field diffusive coupling on suppression of oscillations for systems of limit cycle oscillators. We show that this coupling scheme not only induces amplitude death (AD) but also oscillation death (OD) in coupled identical systems. The suppression of oscillations in the parameter space crucially depends on the value of mean-field diffusion parameter. It is also found that the transition from oscillatory solutions to OD in conjugate coupling case is different from the case when the coupling is through similar variable. We rationalize our study using linear stability analysis.

We investigate the influence of diversity on the temporal regularity of spiking in a ring of coupled model neurons. We find diversity-induced coherence in the spike events, with an optimal amount of parametric heterogeneity at the nodal level yielding the greatest regularity in the spike train. Further, we investigate the system under random spatial connections, where the links are both dynamic and quenched, and in all the cases we observe marked diversity-induced coherence. We quantitatively find the effect of coupling strength and random rewiring probability, on the optimal coherence that can be achieved under diversity. Our results indicate that the largest coherence in the spike events emerge when the coupling strength is high, and when the underlying connections are mostly random and dynamically changing.