Controlling probability distributions in a noise-driven dynamical system with correlated noise sources

The analysis of probability distributions in the phase space of a noise-driven dynamical system provides important insights into its variability and predictability. Here we analyze the probability density ellipse in the two dimensional phase space of a noise-driven electrical circuit that is composed of two identical RC circuits coupled together with a capacitor. The elliptical shape results from the two RC circuits having different input noise intensities. The voltages across the coupling capacitor are the phase space coordinates that we analyzed. Each RC circuit is driven by a variable linear combination of two independent noise sources.We find that with certain linear combinations the probability density ellipse will narrow, equalizing the voltages on either side of our coupling capacitor and thus removing a large portion of noise in the phase diagram of our system. We quantify the narrowing of the probability density ellipse using two methods: 1) We graph the aspect ratio of the ellipse for many different linear combinations and 2) We analyze the area enclosed within the most probable escape and relaxation path to a target point. Our method illustrates a way to reduce output noise in a system by simply adding a new noise source.