Séminaire SPACE Tours
Asymptotic behavior of solutions of stochastic differential equations with markov switching and applicationsNguyen Huu Du (Vietnam institute for advanced study in mathematics)
Monday 15 December 2025 14:30 - Tours - E2 1180
Résumé :
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.
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