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Bistability in neural oscillators induced by asymmetric electrical coupling

Alexander N. Pisarchik, Mariano Alberto García-Vellisca, Rider Jaimes-Reátegui, Francisco de Pozo-Guerrero
In this work we are interested in the question of how regularity can be broken and how bistability can be induced 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 unidirectionally 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 asymmetry in electrical coupling between periodically spiking neural oscillators induces bistability in the system. One of the coexisting attractors is a limit cycle similar to the original attractor of the uncoupled neuron, while the other one is either a chaotic attractor or another periodic orbit which periodicity
depends on the coupling strength. When the coupling is sufficiently strong, the neurons are completely synchronized in a monostable periodic regime similar to the regime of the solitary neuron.
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