Behavior near the extinction time for systems of differential equations with sublinear dissipation terms
Luan Thach Hoang · arXiv (Cornell University) · 2022
This paper is focused on the behavior near the extinction time of solutions of systems of ordinary differential equations with a sublinear dissipation term. Suppose the dissipation term is a product of a linear mapping $A$ and a positively homogeneous scalar function $H$ of a negative degree $-α$. Then any solution with an extinction time $T_*$ behaves like $(T_*-t)^{1/α}ξ_*$ as time $t\to T_*^-$, where $ξ_*$ is an eigenvector of $A$. The result allows the higher order terms to be general and the nonlinear function $H$ to take very complicated forms. As a demonstration, our theoretical study is applied to an inhomogeneous population model.