Strange Nonchaotic Responses of the Quasiperiodically Forced Morris-Lecar Neuron

We study dynamical responses of the self-oscillating Morris-Lecar (ML) neuron under quasiperiodic stimulation. For the case of periodic stimulation on the self-oscillating ML neuron, a transition from a periodic to a chaotic oscillation occurs through period doublings. We investigate the effect of the quasiperiodic forcing on this period-doubling route to chaotic oscillation. In contrast to the periodically-forced case, a new type of strange nonchaotic (SN) oscillating states (that are geometrically strange but have no positive Lyapunov exponents) is thus found to appear between the regular and chaotic oscillating states. Strange fractal geometry of these SN oscillating states, which is characterized in terms of the phase sensitivity exponent and the distribution of local finite-time Lyapunov exponent, leads to aperiodic “complex” spikings. Diverse routes to SN oscillations are found, as in the quasiperiodically forced logistic map.