Dynamics and synchronization of the Morris-Lecar model with field coupling subject to electromagnetic excitation

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In this study, we extend the Morris-Lecar (M-L) neuron model to design a neuronal network model with field effects. Using Lyapunov theory and the master stability function to evaluate the stability of synchronous manifolds. The Hamilton energy function of a single neuron is derived using Helmholtz's theorem to equivalently describe its internal field energy, and bioelectric activities are analyzed in conjunction with synchronization error functions. A comprehensive analysis was conducted using various numerical methods, including time series diagrams, bifurcation diagrams, two-parameter plane synchronization error diagrams, and similarity function diagrams. The observations indicate that variations in conductivity and equilibrium potential directly impact the firing patterns and synchronization states of neurons. In various coupling methods, an increase in coupling strength induces different degrees of oscillation within the coupled system. The effects of three coupling methods on the synchronization of the neuronal network are examined using spatiotemporal evolution diagrams and energy evolution diagrams. Global synchronization error and synchronization factors are introduced to quantify the level of synchrony. Numerical results indicate that an appropriate coupling strength and ionic conductance enhance network synchrony. Numerical results indicate that appropriate coupling strength promotes network synchrony. The insights gained from this study contribute to providing a more coherent framework for constructing neuronal network models under field-coupled conditions, thereby enhancing the understanding of fundamental principles in neuroscience and offering new perspectives for the treatment and rehabilitation of neurological disorders.