additive noise

Purpose. Measurement of correlation dimension is considered in a dynamic system with additive random noise. To determine the correlation dimension correctly, it is necessary to eliminate the shift of horizontal coordinate in the graph of the correlation integral caused by the increase in distance between the points due to addition of random noise. Methods.

The effect of noise on the self­sustained oscillator near subcritical Andronov–Hopf bifurcation is studied in numerical and full­scale experiments. Van der Pol oscillator is chosen as base model for investigation. The influence of both additive and multiplicative Gaussian white noise is considered. The regularities of evolution of the probability distribution in the self­sustained oscillator are analyzed with increase of the noise intensity for the cases of additive and parametric noise.

Pattern formation due the presence of additive dichotomous fluctuations is studied an extended system with diffusive coupling and a bistable FitzHugh–Nagumo kinetics. The fluctuations vary in space and/or time being noise or disorder, respectively. Without perturbations the dynamics does not support pattern formation. With proper dichotomous fluctuations, however, the homogeneous steady state is destabilized either via a Turing instability or the fluctuations create spatial nuclei of an inhomogeneous states.