一类脉冲反应扩散系统的行波和传播速度  

Traveling waves and spreading speed to impulsive reaction-diffusion models

作　　者：沈林[1] 周红玲[1] 

机构地区：[1]黄淮学院数学科学系,河南驻马店463000

出　　处：《山东科学》2017年第3期88-93,共6页Shandong Science

基　　金：国家自然科学基金(11371164);国家自然科学基金委员会河南省人民政府人才培养联合基金(U1304104)

摘　　要：讨论了开放环境中一类具有固定脉冲时刻的反应扩散系统的传播速度和行波解。在空间分布均匀条件下,给出了正常数解存在和稳定的条件。得到了脉冲反应扩散系统传播速度的具体表达形式,当满足一定条件时,传播速度大于零,该速度也是系统存在行波解的最小速度。以水流速度为参数对系统进行了数值模拟,结果表明通过控制扩散系数、水流速度、离散和连续时间的死亡率和出生率,可实现生物种群的传播和持久生存。In this paper, an impulsive reaction-diffusion model with fixed moments of impulses in an unbounded domain was proposed, and the existence of spreading speed and traveling wave solutions for the model were established. First, the existence and the stability of the positive constant solutions were proved in ODE system. Second, the explicit formula of spreading speed to impulsive reaction-diffusion model was given. When certain conditions were satisfied, the spreading speed was greater than zero, which was the minimum speed of the traveling wave solutions. Finally, the numerical simulation of the system was carried out with the velocity of the water flow. The results reveal that the spread and persistence dynamics of the biotic population can be realized through the control of diffusion coefficient, flow velocity, mortality and birthrate corresponding to discrete time and continuous time respectively.

关 键 词：脉冲反应扩散系统 传播速度 行波 

分 类 号：O175.26[理学—数学]