Dynamical hysteresis in a self-oscillating polymer gel.

An ionic polymer gel may undergo rhythmical swelling-deswelling kinetics induced by chemical oscillation. We demonstrate that the gel admits of dynamical hysteresis, which is manifested in the non-vanishing area of the response function--concentration (of reaction substrate) hysteresis loop, the response function being the integrated probability of residence of the polymer in any one of the swelled or deswelled states. The loop area depends on temperature and exhibits a turnover as a function of the strength of thermal noise--a phenomenon reminiscent of stochastic resonance. The numerical simulations agree well with our proposed analytical scheme.