脉冲-扩散竞争种群动力系统的研究

Research on Impulse-Diffusion Competition System in Population Dynamics

研究了由脉冲 扩散方程组描述的具有即时收获或放养的两竞争种群动力系统的数学模型.建立了研究模型的单调方法,该方法定义了系统的上下解,证明了上下解的有序性,上下解的存在可以保证解的存在,且可利用上下解对解进行估计.获得了利用脉冲常微分方程组作为控制系统,以它的解作为上下解的一些比较结果,以及系统具有渐近性、稳定性的条件.该模型的研究方法可应用于一般的拟单调非增系统,其研究结果对于定量描述和控制实际种群生态系统具有理论指导意义.

The mathematical model of two competing species dynamical system with instantaneous harvesting or stocking is investigated. The model is described by a coupled system of reactiondiffusion equations together with some initial, boundary and impulse conditions. The definition of upperlower solution is given and the monotonic method is established. The order property of supperlower solution is achieved, and it is proved that the existence of upperlower solution ensures the existence of the solution and can be used to estimate the solution. Some comparison results about the solutions and the conditions for the asymptotic property and stability of the system are obtained by using the solutions of dominating impulsive ordinary differential equation as supper and lower solution. The research method can be applied to other quasimonotone nonincreasing system, and the results obtained are theoretically significant to describe quantitatively and control the ecological system of the real population.