DICHOTOMOUSLY SWITCHED PHASE FLOWS

The general formalism for periodic dichotomous noise on nonpotential f lows is considered. This uncorrelated noise process switches suddenly at integer values of period tau. The effect of additive noise of this kind on the planar FitzHugh-Nagumo ordinary differential equations [R. FitzHugh, Biophys. J. 1, 445 (1961), J. Nagumo, S. Arimoto, and Y. Yo shikawa, Proc. IRE 50, 2061 (1962)] is examined. For large tau, quasif ractal attractors are observed, whereas for the white-noise limit, whe re tau is small. a Fokker-Planck equation describes the evolution. The magnitude of tau determines the smoothness of the transient evolution and equilibrium density of the system. Typically the stochastic equat ions give rise to two regions of high density near the stable fixed po ints of the underlying autonomous system. The stiffness parameter epsi lon in the differential equations determines the fast variable, its as sociated nullcline, and the resulting flow structure. For small epsilo n the cubic nullcline controls the motion and transitions between the high-density peaks occur along segments of a noisy limit cycle. For la rge epsilon the linear nullcline governs the transitions and the peaks are joined by a single band. The statistical behavior of the oscillat ory and direct transitions is examined.