Complex network dynamics of a memristor neuron model with piecewise linear activation function

Neurons are the key players in the brain; it is estimated that approximately 86 billion neurons are used to transfer the information among brain cells and to all other body parts. These neurons formulated as an incredibly complex network and exhibits intricate dynamical behaviors ever known. The membrane capacitance and resistance plays vital role in current flow through the neuron hence while it is exposed to any electromagnetic field, the charges under goes abrupt changes. In this work, we investigated a 2D piecewise linear learning neuron model with periodic excitation and magnetic flux coupling. A quadratic memductance function is considered for the magnetic flux coupling relation. We derived the bifurcation plot and Lyapunov spectrum for different values of the excitation amplitude and observed the transition between periodic oscillations and chaotic oscillation. To study the wave propagation dynamics, a single layer lattice array of the neuron is constructed as a M x M network with M = 110. The higher values of excitation amplitude, the network exhibits highly turbulent exotic waves with several wave reentries. The spatiotemporal snapshots are presented by calculating the sample entropy of the network to show the excitability changes of the individual nodes in the network. In addition, we provided phase plane plots to clarify the multi-period oscillations of the nodes. Then, we extended our investigation to understand the influence of flux coupling coefficient on the wave propagation. To capture the complexity changes in the nodes for the different values of the flux coupling coefficient, corresponding sample entropy is derived and plotted. Sample entropy has significant advantages such as data length independence. The results obtained in this work reinforced the importance of simple 2D piecewise linear learning neuron model to mimic various dynamical scenario in neuromorphology and the interplay between ionic currents particularly in a network scheme. Unlike the previous studies, we supplied the excitation at the center of the network and considered no flux boundary conditions which pushes the system more closer to the real neuron. The method of calculating sample entropy in the nodes for investigating the complexity changes is discussed in very few literature; with this research work, we nailed the importance of complexity analysis in wave propagation and influence of excitation amplitude and magnetic flux coupling.