Adaptive transitions in FitzHugh-Nagumo networks with Hebb-Oja coupling rules

Abstract

Adaptive coupling in networks of interacting neurons has gained recent attention due to the many applications both in biological and in artificial neural networks, where adaptive coupling or synaptic plasticity is considered as a key factor in learning processes. In the present study, we apply adaptive connectivity rules in networks of interacting FitzHugh-Nagumo oscillators. Adaptive coupling, here, is realized via Hebbian learning adjusted by the Oja rule to prevent the network link weights from growing without bounds. Numerical investigations demonstrate that during the adaptation process the FitzHugh-Nagumo network undergoes adaptive transitions realizing traveling waves, synchronized states and chimera states transiting through various multiplicities. These transitions become more evident when the time scales governing the coupling dynamics are much slower than the ones governing the nodal dynamics (nodal potentials). Namely, when the coupling time scales are slow, the network has the time to realize and demonstrate different synchronization regimes before reaching the final steady state. The transitions can be observed not only in the spacetime plots but also in the abrupt changes of the average coupling weights as the network evolves in time. Regarding the asymptotic coupling distributions, we show that the limiting average coupling strength follows an inverse power law with respect to the Oja parameter (also called "forgetting" parameter) which balances the learning growth. We also report abrupt transitions in the asymptotic coupling strengths when the parameter related to adaptive coupling crosses from fast to slow time scales. These findings are in line with previous studies on spiking neural networks.