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Rotating wave dynamics and multistability in a unidirectional ring of Hindmarsh–Rose neurons

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  • Pisarchik, Alexander N.

Abstract

Wave dynamics and synchronization are investigated in a unidirectional ring of Hindmarsh–Rose neural oscillators with excitatory chemical synaptic coupling. Stationary regimes are analyzed to determine how the wave speed and the number of waves in the ring depend on the control parameters, specifically the coupling strength and external current, and on the initial conditions. Time series, bifurcation, and spatiotemporal analyses of the membrane potential, inter-burst intervals, and energy demonstrate very rich dynamics, including the coexistence of various regimes in the ring network, such as regular waves with different mode-locking ratios, interval running waves with variable speed, standing waves, and chimeric waves. The results provide insights into possible mechanisms underlying structured activity in neural circuits and offer a versatile testbed for studying wave-mediated information processing.

Suggested Citation

  • Pisarchik, Alexander N., 2026. "Rotating wave dynamics and multistability in a unidirectional ring of Hindmarsh–Rose neurons," Chaos, Solitons & Fractals, Elsevier, vol. 210(P1).
    • Handle: RePEc:eee:chsofr:v:210:y:2026:i:p1:s0960077926007460
    DOI: 10.1016/j.chaos.2026.118605
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