Noise-free Stochastic Resonance in Simple Chaotic Systems

The phenomenon of Stochastic Resonance (SR) is reported in a completely noise-free situation, with the role of thermal noise being taken by low-dimensional chaos. A one-dimensional, piecewise linear map and a pair of coupled excitatory-inhibitory neurons are the systems used for the investigation. Both systems show a transition from symmetry-broken to symmetric chaos on varying a system parameter. In the latter state, the systems switch between the formerly disjoint attractors due to the inherent chaotic dynamics. This switching rate is found to ``resonate'' with the frequency of an externally applied periodic perturbation (either parametric or additive). The existence of a resonance in the response of the system is characterized in terms of the residence-time distributions. The results are an unambiguous indicator of the presence of SR-like behavior in these systems. Analytical investigations supporting the observations are also presented. The results have implications in the area of information processing in biological systems.