Bistability in Hindmarsh-Rose oscillators induced by asymmetric electrical coupling
Rider Jaimes-Reátegui, Mariano Alberto García-Vellisca, Alexander Pisarchik, Francisco del Pozo-Guerrero
In this paper, we are interested in the question of how bistability can appear in coupled neurons. Concrete motivation for such a general problem is the search for a way to destroy an organism having a stable dynamics by destabilizing its metabolism. To address this issue, we consider the model of a pair of neuron cells coupled via an electrical synapse. We focus on the Hindmarsh-Rose model which provides a simple description of the patterned activity observed in molluscan neurons. The results of numerical simulations show that asymmetric electrical coupling between periodically spiking neural oscillators results in bistability in this system. One of the coexisting attractors is a limit cycle similar to the attractor of the uncoupled neuron, while the other one can be either a chaotic or a periodic orbit depending on the coupling strengths. Bistability is only observed for relatively small couplings. When the coupling is sufficiently strong, the neurons are in a monostable periodic regime, similar to the spiking regime observed in the uncoupled neurons.
CYBERNETICS AND PHYSICS, Vol. 6, No. 3. 2017, 126-130