Noise dependent synchronization of a degenerate SDE
Isabell Vorkastner
TL;DR
This paper investigates how the strength and directions of degenerate additive noise in a stochastic differential equation influence synchronization, demonstrating that synchronization can occur or not depending on noise parameters and Lyapunov exponents.
Contribution
It provides a specific example of a degenerate SDE showing how noise characteristics determine synchronization behavior, highlighting the role of the top Lyapunov exponent.
Findings
Synchronization depends on noise strength and directions
Sign change of Lyapunov exponent indicates synchronization transition
Weak random attractor can be a single random point
Abstract
We provide an example of an SDE with degenerate additive noise where synchronization depends on the strength of noise and the number of directions in which the noise acts. Here, synchronization means that the weak random attractor consists of a single random point. Indicated by a change of sign of the top Lyapunov exponent, we prove synchronization respectively no (weak) synchronization.
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