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 $\omega$, 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.

6 pages LaTex, 4 figures

References in corpus (4)

• Stochastic Resonance in Deterministic Chaotic Systems
• Stochastic Resonance in Chaotic Spin-Wave Dynamics
• Kinetic Ising System in an Oscillating External Field: Stochastic Resonance and Residence-Time Distributions
• Stochastic Resonance in Maps and Coupled Map Lattices

Cited by in corpus (5)

• Noise-free Stochastic Resonance in Simple Chaotic Systems
• Combined effects of STDP and homeostatic structural plasticity on coherence resonance
• Response to sub-threshold stimulus is enhanced by spatially heterogeneous activity
• Bilinear effect in complex systems
• Chaotic Dynamics in Iterated Map Neural Networks with Piecewise Linear Activation Function