Dang H. Nguyen

Stochastic population growth in spatially heterogeneous environments: the density-dependent case

This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for resources, spatio-temporal heterogeneity and dispersal. The population is spread throughout n patches whose population abundances are modeled as the solutions of a system of nonlinear stochastic differential equations living on

Stochastic Lotka–Volterra food chains

[0,\infty )^n

Asymptotic harvesting of populations in random environments

[0,∞)n. We prove that r, the stochastic growth rate of the total population in the absence of competition, determines the long-term behaviour of the population. The parameter r can be expressed as the Lyapunov exponent of an associated linearized system of stochastic differential equations. Detailed analysis shows that if

The competitive exclusion principle in stochastic environments

r>0

Switching diffusion with past dependent switching and countable switching space: Existence and uniqueness of solutions, recurrence, and weak stabilization

r>0, the population abundances converge polynomially fast to a unique invariant probability measure on