Chimera states, synchronization, and energy consumption in a chaotic electrically coupled Hindmarsh–Rose neural network under multiple memory effects

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Abstract
We investigate memory-induced collective dynamics in a ring of electrically coupled Hindmarsh–Rose neurons operating in a chaotic bursting regime. The effects of long-range interactions, diffusion delay, reaction delay, and electromagnetic induction on spatiotemporal organization and Hamiltonian energy density are systematically analyzed. The dynamics is quantified using five complementary statistical indicators: the synchronization factor, the strength of incoherence, the discontinuity measure, the skewness measure, and the time-averaged Hamiltonian energy density. Depending on the memory parameters, the network exhibits asynchronous, chimera, multichimera, and synchronized states. We show that long-range interactions increase the Hamiltonian energy density and enhance the level of collective activity, although they predominantly generate asynchronous states when acting alone. Diffusion delay generates a rich variety of collective states, ranging from asynchronous and chimera patterns to complete synchronization depending on the interaction range, while reaction delay predominantly supports asynchronous, chimera, and multichimera dynamics. In contrast, electromagnetic induction promotes global synchronization from a critical memristive coupling threshold. Furthermore, the Hamiltonian energy density increases monotonically with the interaction range, reaction delay, and memristive feedback strength, whereas it exhibits a non-monotonic dependence on diffusion delay. These findings demonstrate that multiple memory mechanisms interact synergistically and competitively to shape neuronal coordination, energy localization, and pattern formation, providing new insights into the design of robust neuromorphic systems and brain-inspired algorithms.

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