Deterministic SR in a Piecewise Linear Chaotic Map

Abstract

The phenomenon of Stochastic Resonance (SR) is observed in a completely deterministic setting - with thermal noise being replaced by one-dimensional chaos. The piecewise linear map investigated in the paper shows a transition from symmetry-broken to symmetric chaos on increasing a system parameter. In the latter state, the chaotic trajectory switches between the two formerly disjoint attractors, driven by the map's inherent dynamics. This chaotic switching rate is found to `resonate' with the frequency of an externally applied periodic perturbation (multiplicative or additive). By periodically modulating the parameter at a specific frequency $ω$, we observe the existence of resonance where the response of the system (in terms of the residence-time distribution) is maximum. This is a clear indication of SR-like behavior in a chaotic system.