Generalized multiplicative stochastic processes arising from one-dimensional maps with noise

AbstractWe propose a class of generalized multiplicative stochastic processes obtained by introducing an endo-perspective into one-dimensional maps with additive noise. We define an internal state for the noisy dynamics of a given one-dimensional map and study its statistical behavior. We found intermittency characterized by two power-laws in the dynamics of the internal state for the logistic map and the BZ map with noise which exhibit different noise-induced phenomena, namely, noise-induced chaos and noise-induced order, respectively. We show that the power-laws can be explained in a unified way from the theory of generalized multiplicative stochastic processes.