Stochastic resonance and self-tuning: A simple threshold system

To put it in the framework of information processing, stochastic resonance (SR) is a phenomenon in which the transfer of information from input to output signals can be significantly increased by noise with appropriate (nonzero) intensity. The minimum requirements for SR are generally input signals, nonlinearity, and noise, in addition to a quantifier to measure the efficiency of information transfer. We study a simple threshold system and propose an adaptation mechanism for system parameters, such as a threshold and noise intensity (i.e., temperature), which are held fixed in a normal SR setting. Our emphasis is put on parameter dynamics induced by this adaptation, which we call self-tuning (ST), and on how this dynamics modifies or changes the SR picture with respect to information processing efficiency. As a measure for performance of the threshold system we take mutual information and the signal-to-noise ratio. These quantities are calculated by an analytical method and by a simulational one. ST of temperature results in oscillatory time variation in temperature with its average located around the temperature at which performance is maximized in the SR setting. ST of a threshold turns out to improve performance in the weak noise region.