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<p>Bursting oscillations present a fundamental neural firing pattern that plays a crucial role in information processing. However, the underlying mechanisms governing their generation and synchronization within heterogeneous neuronal networks remain incompletely understood. In this study, we examine a memristive synapse-coupled neuronal network composed of a FitzHugh-Nagumo (FHN) neuron and a Morris-Lecar (ML) neuron. Through numerical simulations and phase-plane analysis, we systematically investigate how changes in coupling strength affect the overall dynamics of the network. Our research findings indicate that as the coupling strength increases, the dynamic state undergoes a significant transition—from asynchronous bursting to fully synchronized bursting. Two distinct bursting mechanisms are identified: (1) asynchronous composite bursting arising from a bifurcation cascade involving fold, subcritical Hopf, supercritical Hopf, and homoclinic bifurcations; and (2) synchronized bursting triggered exclusively by strong inter-neuronal coupling, independent of bifurcation processes. Phase-plane analysis further reveals that under weak coupling conditions, the nonlinearity of the neurons themselves dominates, resulting in their membrane potential nullclines respectively display characteristic <i>N</i>-shaped (FHN) and <i>S</i>-shaped (ML) configurations. In the case of strong coupling, linear interactions become predominant, leading to nullcline convergence, alignment of fixed points, and ultimately complete synchronization between the two heterogeneous neurons. Finally, Multisim circuit simulation results are presented to validate the firing dynamics of the memristive synapse-coupled neuronal network.</p>

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Bursting generation and synchronization mechanisms of a heterogeneous neuronal network with memristor synapse

  • 期刊论文

  • 发表日期：

    2026年3月5日

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  • Luyao Tong,
  • Zhijun Li,
  • Jieqiong Zhu

摘要

Bursting oscillations present a fundamental neural firing pattern that plays a crucial role in information processing. However, the underlying mechanisms governing their generation and synchronization within heterogeneous neuronal networks remain incompletely understood. In this study, we examine a memristive synapse-coupled neuronal network composed of a FitzHugh-Nagumo (FHN) neuron and a Morris-Lecar (ML) neuron. Through numerical simulations and phase-plane analysis, we systematically investigate how changes in coupling strength affect the overall dynamics of the network. Our research findings indicate that as the coupling strength increases, the dynamic state undergoes a significant transition—from asynchronous bursting to fully synchronized bursting. Two distinct bursting mechanisms are identified: (1) asynchronous composite bursting arising from a bifurcation cascade involving fold, subcritical Hopf, supercritical Hopf, and homoclinic bifurcations; and (2) synchronized bursting triggered exclusively by strong inter-neuronal coupling, independent of bifurcation processes. Phase-plane analysis further reveals that under weak coupling conditions, the nonlinearity of the neurons themselves dominates, resulting in their membrane potential nullclines respectively display characteristic N-shaped (FHN) and S-shaped (ML) configurations. In the case of strong coupling, linear interactions become predominant, leading to nullcline convergence, alignment of fixed points, and ultimately complete synchronization between the two heterogeneous neurons. Finally, Multisim circuit simulation results are presented to validate the firing dynamics of the memristive synapse-coupled neuronal network.