Hamilton energy, complex dynamical analysis and information patterns of a new memristive FitzHugh-Nagumo neural network

This paper presents and studies the dynamics of a single neuron, followed by the network of an improved FitzHugh-Nagumo model with memristive autapse. The investigation on the single neuron revealed that, for the set of the system parameters used for our study, the improved model experiences hidden dynamics. The Hamilton energy of the proposed model is established by exploiting the Helmholtz theorem. It is found that the external current has no effect on that energy and only the memristive autapse strength is able to affect the energy released by the considered neuron. The study of the dynamics of the proposed model revealed neuronal behaviors such as quiescent, bursting, spiking, and hysteretic dynamics characterized by the coexistence of firing patterns for the same set of parameters. The electronic circuit of the proposed model is constructed and simulated in the Pspice environment, and the obtained results match well with those obtained from the direct investigations of the mathematical model of the introduced neuron. Furthermore, a chain network of 500 identical neurons with memristive autapses is built and information pattern stability is investigated numerically via modulational instability under memristive autapse strength. It is found that with initial conditions taken as slightly modulated plane waves, the new network supports localized information patterns with traits of synchronization as a means of information coding. Also, by fixing the stimulation current, higher autaptic couplings resulted in new localized pattern formation, confirming the new information coding pattern and possible mode transition. This could provide a possible application in the building of artificial neurons.