6 problems

Consider a two-patch metapopulation with a homoclinic connection in its phase space, and suppose that this connection attracts nearby initial conditions. Assume that one of the two…

Consider a deterministic two-patch metapopulation model with diffusion parameter $D$, whose origin may be a source or a saddle equilibrium, and whose patch populations can approach…

Consider the resource-supplemented logistic network model … where $\bar r_i$ is the intrinsic growth rate, $r_i$ is the increase due to resource supplementation, and $q$ is the dri…

Let $r_1,r_2,r_3\geq 0$ be the growth-rate resources with $r_1+r_2+r_3=r$, and let $\rho$ denote the metapopulation growth rate for the tributary, straight, or distributary three-p…

Consider a multi-patch frequency-dependent SIS epidemic model, with $R_{0}$ denoting its basic reproduction number and with infective individuals moving between patches at a specif…

Local persistence criterion. If there is global persistence, then local persistence occurs only if