Abstract
Stochastic resonance (SR) is an effect that has been known (Benzi, R., Sutera, A., and Vulpiani, A. (1981), ‘The Mechanism of Stochastic Resonance’, Journal of Physics, A14, L453–L457) for almost three decades and has been extensively studied in biology, statistics, signal processing and in numerous other eclectic areas (Wiesenfeld, K., and Moss, F. (1995), ‘Stochastic Resonance and the Benefits of Noise: From Ice Ages to Crayfish and Squids’, Nature, 373, 33–36). Herein, a nonlinear control theory analysis is conducted on how to better understand the class of systems that may exhibit the SR effect. Using nonlinear control theory methods, equilibrium points are manipulated to create the SR response (similar to shaping dynamical response in a phase plane). From this approach, a means of synthesising and designing the appropriate class of nonlinear systems is introduced. New types of nonlinear dynamics that demonstrate the SR effects are discovered, which may have utility in control theory as well as in many diverse applications. A numerical simulation illustrates some powerful attributes of these systems.
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