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Spiral wave analysis in bidirectional Hindmarsh–Rose neurons with nonlinear coupling and dynamical control through external magnetic induction

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  • Debnath, Sajal
  • Kundu, Santimoy

Abstract

The electrical, physical, structural and chemical characteristics of neurons combine to develop very complex dynamical systems. A valuable approach for addressing such high levels of complexity is the investigation of brain spatiotemporal patterns. In this work, two neural systems connected by a nonlinear synapse initiate to manage the stability of synchronization and mode transition in neurons that are in phase lock. In order to activate two neural systems via nonlinear coupling, chaotic signals are encoded to represent separated waves with a restricted frequency range. We have particularly concentrated on the spiral spatiotemporal pattern for the purpose of our investigation. A substantial influence of spirals is made to certain brain functions. We investigate the different dynamical characteristics for the coupled neuronal model, considering the flux coupling constant and coupling coefficients for account as control factors. The results demonstrated that nonlinear coupling through certain components prevents bursting between neurons generated by filtered chaotic inputs and is useful in the creation of nonlinear synapses. In the end, we will examine the impact of amplitude and frequency of an external force on the dynamics of a spiral wave inside a neural network for controlling the wave.

Suggested Citation

  • Debnath, Sajal & Kundu, Santimoy, 2026. "Spiral wave analysis in bidirectional Hindmarsh–Rose neurons with nonlinear coupling and dynamical control through external magnetic induction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 683(C).
    • Handle: RePEc:eee:phsmap:v:683:y:2026:i:c:s037843712500857x
    DOI: 10.1016/j.physa.2025.131205
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