Dynamical analysis of a novel 4-neurons based Hopfield neural network: emergences of antimonotonicity and coexistence of multiple stable states

Abstract

In this contribution, we investigate the dynamics of a novel model of 4-neurons based Hopfield neural networks. Our analyses highlight complex phenomena such as chaotic and periodic behaviors which have been classified by Panahi et al. (Chaos Solitons Fractals 105:150–156, 2017) as some brain behaviors. More interestingly, it has been revealed several sets of synaptic weights matrix for which the proposed HNNs displays multiple coexisting stable states including two, four and six disjoined orbits. Basins of attraction of coexisting stable states have been computed showing different regions in which each solution can be captured. Beside the presence of coexisting bifurcations, the model displays remerging Feigenbaum trees bifurcations also known as antimonotonicity for some judicious sets of synaptic weights. PSpice investigations are finally used to confirm results of the theoretical investigations.