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- W2062601725 abstract "We study the top Lyapunov exponent of the response of a two-dimensional non-Hamiltonian system driven by additive white noise. The origin is not a fixed point for the system; however, there is an invariant measure for the one-point motion of the system. In this paper we consider the stability of the two-point motion by Khasminskii's method of linearization along trajectories. The specific system we consider is the third-order truncated normal form of the unfolding of a Hopf bifurcation. We show that in the small noise limit the top Lyapunov exponent always approaches zero from below (and is thus negative for noise sufficiently small); we also show that there exist open sets of parameters for which the top Lyapunov exponent is positive. Thus the two-point motion can be either stable or unstable, while the stationary density that describes the one-point motion always exists." @default.
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- W2062601725 date "2011-01-01" @default.
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- W2062601725 title "Stability of a Stochastic Two-Dimensional Non-Hamiltonian System" @default.
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- W2062601725 doi "https://doi.org/10.1137/100782139" @default.
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