| We consider delayed stochastic systems driven by different stochastic model processes: dichotomous Markov process and Gaussian white noise which couple to the system in additive or multiplicative way. We are interested to find the threshold of stability considering different stability criteria. As an effect of the noise, the threshold may be shifted due to the noise compared with the corresponding deterministic system. It is found that, at the threshold of stability, the probability density of the return times to a certain arbitrary level is a power law. In some cases it is possible to calculate the characteristic exponent analytically. The analytical results are corroborated by numerical simulations. Joint work with Micaela Krieger, Christian Brettschneider, and Lucas Wetzel. |
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