  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.
