Emergence of chimera states in neural networks with distance-dependent mean field coupling

The emergence of chimera states in neural networks has been an interesting area of research in the past few years and aims to explore the complex brain functions. Even though the presence of chimera states in systems with nonlocal interaction is well known, its emergence in networks with global and local interactions is least explored. Different techniques like introducing distance dependent interactions and restricting initial conditions to certain classes are adopted to induce chimera states in such network. This work analyzes methods to induce chimera or multichimera states in a network of mean field coupled Hindmarsh-Rose neurons in ring topology. The interaction schemes in the network, viz., global, nonlocal and local are realized by limiting the number of neurons involved in coupling and the power law exponent gives a distance gradient effect to them. The studies have shown that, in global interaction, power law exponent induces chimera states and reduces the amount of synchrony in the network. The nonlocal coupling is self-capable of inducing chimera states and power law exponent enhances the capability. When the value of power law exponent is high, the synchrony level is independent of the number of neurons taking part in the coupling. The traveling chimera states are induced in the local (nearest neighbor) coupling by modifying the initial conditions.