Complex dynamics of a heterogeneous network of Hindmarsh-Rose neurons

TL;DR

This paper explores the complex collective behaviors of heterogeneous Hindmarsh-Rose neuron networks, revealing new spatiotemporal patterns, chimera states, and validating findings through electronic circuit simulations.

Contribution

It introduces the study of heterogeneous HR neuron networks with novel spatiotemporal patterns and chimera states, supported by electronic circuit validation.

Findings

Rich dynamics including chaos, bursting, and spiking observed.

Discovery of new clustered chimera states in heterogeneous networks.

Electronic circuit model matches mathematical simulations.

Abstract

In this contribution, we have considered the collective behavior of the two as well as the network of heterogeneous coupled Hindmarsh Rose (HR) neurons. The heterogeneous models were made of a memristive 2D (HR) and the traditional 3D HR neurons. Investigating a model of two coupled neurons through an electrical synapse reveals dissipative properties. When control parameters are varied, the coupled neuron model exhibits rich dynamics, such as the periodic, quasi-periodic, and chaotic dynamics involving either bursting or spiking oscillations. For weak electrical coupling strength, non-synchronized motion is observed. But in the case of higher coupling strength, synchronized cluster states are observed. Besides, ring-star networks of up to 100 under three different heterogeneous topologies are being investigated, and various spatiotemporal patterns are explored. It is found that the spatiotemporal patterns depend on the topology of the heterogeneous network considered. A new clustered chimera state is revealed qualitatively via the recurrence plot. The cluster states are indicated in the ring and star configurations of the heterogeneous network. Single and double-well chimera states have been revealed in the ring and ring-star structures. Finally, an equivalent electronic circuit for the two coupled heterogeneous is designed and investigated in the PSIM simulation environment. A perfect match is observed between the results obtained from the designed analog circuit and the mathematical model of the two coupled neurons, which supports the fact that our obtained results are not related to an artifact.