Two-state theory of nonlinear Stochastic Resonance
Jes\'us Casado-Pascual (1), Jos\'e G\'omez-Ord\'o\~nez (1), Manuel, Morillo (1), Peter H\"anggi (2)((1) F\'isica Te\'orica, Universidad de, Sevilla, Spain, (2) Institut f\"ur Physik, Universit\"at Augsburg, Germany)
TL;DR
This paper presents an analytical two-state model for nonlinear stochastic resonance in bistable systems, deriving explicit formulas for key dynamics and demonstrating conditions for anomalous SR-gains exceeding unity.
Contribution
It introduces a simplified two-state analytical framework for nonlinear stochastic resonance, capturing complex behaviors and matching numerical solutions.
Findings
Analytical expressions for population dynamics and SNR are derived.
Anomalous SR-gains exceeding unity are observed within certain parameters.
Non-monotonic SNR behavior as a function of noise strength is demonstrated.
Abstract
An amenable, analytical two-state description of the nonlinear population dynamics of a noisy bistable system driven by a rectangular subthreshold signal is put forward. Explicit expressions for the driven population dynamics, the correlation function (its coherent and incoherent part), the signal-to-noise ratio (SNR) and the Stochastic Resonance (SR) gain are obtained. Within a suitably chosen range of parameter values this reduced description yields anomalous SR-gains exceeding unity and, simultaneously, gives rise to a non-monotonic behavior of the SNR vs. the noise strength. The analytical results agree well with those obtained from numerical solutions of the Langevin equation.
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