| Abstract: |
| In this talk we investigate whether the random attractor and the Sinai--Ruelle--Bowen (SRB) measure can be preserved under numerical discretization for the stochastic Hopf bifurcation modeled by a nonlinear stochastic differential equation. To this end, we establish that the stochastic Hopf bifurcation under discretization induces a discrete random dynamical system. Further, we prove that this discrete system possesses a random attractor, and then derive the existence of an SRB measure by demonstrating a strictly positive numerical Lyapunov exponent. Numerical experiments visualize the retained random attractor and SRB measure for the discrete random dynamical system, revealing structures consistent with the theoretical chaotic phase. |
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