Asymptotic behavior of solutions of stochastic differential equations with markov switching and applications

par Nguyen Huu Du (Vietnam institute for advanced study in mathematics)

lundi 15 déc. 2025, 14:30 → 15:30 Europe/Paris

E2 1180 (Tours)

This talk deals with some results concerning to the dynamic behavior of a two species in an eco-system, described by Markov regime switching differential equation:
$\dot{x} = xa(\xi(t), x, y)$
$\dot{y} = yb(\xi(t), x, y),$
or by reaction-diffusion equation
$u_t(t, x) = d_1\Delta u(t, x) + ua(\xi(t), u, v)$
$v_t(t, x) = d_2\Delta v(t, x) + vb(\xi(t), u, v)$
where $(\xi(t))$ is a Markov process valued in a finite set $S$, which can be considered as a factor switching environment conditions. We are interested in giving sufficient and almost necessary conditions to the permanence or extinction of solutions by constructing a threshold; describing ω-limit sets, attractors of the system; The ergodicity of systems has been studied in case it is permanent.