Qualitative properties of a cooperative degenerate Lotka-Volterra model

Abstract

This paper considers a kind of degenerate parabolic systems. First, we consider the initial boundary value problem of the two-species degenerate parabolic cooperative system. By using the method of a parabolic regularization and energy estimate, we establish the existence of the weak solution of the problem. Then we establish the comparison principle and discuss the uniqueness and the uniform bound. At last, we consider the periodic boundary value problem of the system. By constructing a pair of ordered upper and lower solutions, we establish the existence of nontrivial nonnegative periodic solutions.

Lyapunov Stability Analysis of a Competition Model with Crowding Eects

“…In interspecific competition species less suited to compete for the resources may die out unless they adapt by character dislocation. In the literature, the well developed and most popular growth laws were established in [5,6,7,8,9,10]. In this paper, we develop a basic competition model based on two different species either intraspecific or interspecific competition with two different growth rates and their carrying capacities are non-identical.…”