| Abstract: |
| We introduce a novel 2-D discrete neuron map, denoted by map H(x,phi), formed by incorporating electromagnetic flux into a one-dimensional Chialvo map. Our exploration encompasses a comprehensive study of the dynamical aspects of the map, covering fixed points, bistability, various bifurcations, S-shape attractor, firing patterns, pathways leading to chaos, including the period-doubling to chaos and reverse period-doubling to chaos. We validate the results by employing various dynamical techniques (like Lyapunov exponent diagrams, phase portraits, calculating the correlation dimensions, and basins of attraction).
Beyond single-neuron analysis, we extend our investigation to a neuron network governed by the map H(x, phi), specifically a ring-star network configuration. This broader examination reveals various dynamical states within the network, including synchronous, asynchronous, and chimera states. Finally, we present simulations exploring different coupling strengths to uncover diverse wavy patterns and clustered states within the network dynamics. |
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