Traveling chimera states in locally coupled memristive Hindmarsh-Rose neuronal networks and circuit simulation

Chimera states have been found in many physiology systems as well as nervous systems and may relate to neural information processing. The present work investigates the traveling chimera states in memristive neuronal networks of locally coupled Hindmarsh-Rose neurons, with both excitation and inhibition considered. Various traveling chimera patterns and firing modes are found to exist in the networks. Particularly, for excitatory connection, two kinds of traveling chimera states appear in opposite directions. Besides, a new type of chimera state composed of traveling chimera state and incoherent state is observed, named the semi-traveling chimera state. Multi-head traveling chimera states with several incoherent groups are also observed. For excitatory-inhibitory connection, the network is observed to exhibit an imperfect coherent state under the synergistic effect of strong excitatory and weak inhibitory coupling. Moreover, a firing pattern named mixed-amplitude bursting state is witnessed, consisting of two bursts of different amplitudes in a time sequence. Furthermore, an electric circuit is designed and built on Multisim to realize the above phenomena, suggesting that traveling chimera states could be generated in real circuits. Our findings can deepen the understanding of the electromagnetic induction effect in regulating the dynamics of neuronal networks and may provide useful clues for constructing artificial neural systems.