Hyperbolic and non-hyperbolic chaos in a pair of coupled alternately excited FitzHugh-Nagumo systems

Abstract: We investigate a possibility of realization of structurally stable chaotic dynamics in neural systems. The considered model of interacting neurons consists of a pair of coupled FitzHugh-Nagumo systems, with the parameters being periodically modulated in antiphase, so that the neurons undergo alternate excitation with a successive transmission of the phase of oscillations from one neuron to another. It is shown that 4D map arising in a stroboscopic Poincare section of the model flow system possesses a hyperbolic strange attractor of the Smale-Williams type. The dynamical regime observed in the system represents a sequence of amplitude bursts, in which the phase dynamics of oscillatory spikes is described by chaotic mapping of Bernoulli type. The results are confirmed by numerical calculation of Lyapunov exponents and their parameter dependencies, as well as by direct computation of the distributions of angles between stable and unstable tangent subspaces of chaotic trajectories.