Bifurcation and persistence in a stochastic seasonal dynamical system

We studied stochastic bifurcation and persistence in seasonally forced dynamical systems governed by stochastic differential equations with periodically switching drift in this paper. By using Lyapunov exponent techniques, we characterized extinction and persistence via a noise dependent threshold determined by the top Lyapunov exponent. Futhermore, we proved that variation of the season length parameter induces a stochastic bifurcation, where stability of the extinction state is lost and nontrivial invariant probability measures emerge. Analytical results were illustrated through a stochastic Lotka-Volterra model, showing that environmental noise shifts extinction persistence thresholds and fundamentally alters long-term dynamics.