  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.
