Extremely rich dynamics of coupled heterogeneous neurons through a Josephson junction synapse

Artificial neural networks are generally used to emulate some biological activities of the brain. Those neurons in the network are connected to others through synapses. As a result, several works have been devoted to the design of various artificial synapses, including the Josephson Junction Synapse (JJS). In this contribution, a model of the Hindmarsh–Rose neuron coupled with a FitzHugh–Nagumo neuron through a JJS is considered. That JJS enables us to simulate the effects of the magnetic field by providing additional phase error between the junctions. The Hamilton function related to the energy released by the coupled neurons during the transition between electrical activities is determined using the Helmholtz theorem. The equilibrium points of the proposed model are investigated, and their stability justifies the self-excited dynamics of the model. During studies, sets of phenomena such as Hopf bifurcation, double Hopf bifurcation, periodic spikings, periodic and chaotic burstings, (resp. firings) are found. More importantly, several coexisting activities are found in the coupled neurons as well as hyperchaotic firing activities rarely reported in such classes of neurons. Finally, PSpice simulations are used to further support results obtained from the mathematical model of coupled neurons through a JJS. •Coupled heterogeneous neurons.•Hamilton energy computation.•Josephson junction synapse.•Extremely rich dynamics.•Circuit implementation.