Abstract
Brain functions are sometimes emulated using some analog integrated circuits based on the organizational principle of natural neural networks. Neuromorphic engineering is the research branch devoted to the study and realization of such circuits with striking features. In this contribution, a novel small network of three neurons is introduced and investigated. The model is built from the coupling between two 2D Hindmarsh–Rose neurons through a 2D FitzHugh–Nagumo neuron. Thus, a heterogeneous coupled network is obtained. The biophysical energy released by the network during each electrical activity is evaluated. In addition, nonlinear analysis tools such as two-parameter Lyapunov exponent, bifurcation diagrams, the graph of the largest Lyapunov exponent, phase portraits, time series, as well as the basin of attractions are used to numerically investigate the network. It is found that the model can experience hysteresis justified by the simultaneous existence of three distinct electrical activities using the same set of parameters. Finally, the circuit implementation of the network is addressed in PSPICE to further support the obtained results.
Highlights
Brain functions are sometimes emulated using some analog integrated circuits based on the organizational principle of natural neural networks (NNN)
That discrepancy is justified by the hysteretic nature of the network for the set of the electrical coupling weights used for the investigations. As it can be seen on those two-parameter Lyapunov exponents, the dynamics of the proposed network is able to vary from periodic firing activities ðkmax 1⁄4 0Þ to chaotic firing activities ðkmax [ 0Þ based on the sign of the maximum Lyapunov exponent
The numerical computation of the equilibria of the proposed network revealed that they are all complex numbers, which implies the possibility for the network to exhibit hidden dynamics
Summary
Brain functions are sometimes emulated using some analog integrated circuits based on the organizational principle of natural neural networks (NNN). Baran et al [26] investigated the phenomenon of spike-timing-dependent-plasticity (STDP) learning using chemical and memristive synapses on two coupled HR neurons Their results were obtained based on numerical simulation, and they showed that in neuromorphic studies of nonlinear processes like chaos and hyperchaos, the memristive device might be employed as an alternative synapse. As a result, traveling chimera states and multicluster oscillating breathers could be found in the absence of the field, whereas chimera states, multichimera states, alternating chimera states, and multicluster traveling chimeras could be found in the presence of the field In all of these works that address neurons, twocoupled neurons, or networks of neurons, energy is required for each firing activity as well as the transition between electrical activities. Most works on coupled neurons or neural network models only considers identical neurons with a single biological function [17, 23, 39, 41,42,43].
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