Evaluation of chaotic resonance by lyapunov exponent in attractor-merging type systems

Abstract

Fluctuating activities in the deterministic chaos cause a phenomenon that is similar to stochastic resonance (SR) whereby the presence of noise helps a non-linear system to amplify a weak (under-barrier) signal. In this phenomenon, called chaotic resonance (CR), the system responds to the weak input signal by the effect of intrinsic chaotic activities under the condition where no additive noise exists. Recently, we have revealed that the signal response of the CR in the spiking neuron model has an unimodal maximum with respect to the degree of stability for chaotic orbits quantified by maximum Lyapunov exponent. In response to this situation, in this study, focusing on CR in the systems with chaoschaos intermittency, we examine the signal response in a cubic map and a chaotic neural network embedded two symmetric patterns by cross correlation and Lyapunov exponent (or maximum Lyapunov exponent). As the results, it is confirmed that the efficiency of the signal response has a peak at the appropriate instability of chaotic orbit in both systems. That is, the instability of chaotic orbits in CR can play a role the noise strength of SR in not only spiking neural systems but also the systems with chaos-chaos intermittency.