【摘要】 给出了一个具有脉冲控制的环境生态数学模型,这个模型考虑的是同一种外界毒素排放到一个封闭的环境中对两个彼此竞争的生物物种的影响,同时生物体不但吸收环境的污染物,而且生物体的排泄将反过来又会污染环境.在此模型中仅考虑外界毒素是常数排放到环境中以及毒素的排放仅对两物种的出生率有影响的情况.在等间距脉冲时刻的情形下,利用脉冲系统的线性近似判定的方法对该模型进行研究,得到了使其渐近稳定到原先不稳定的平衡点的充分条件并给出了生态解释.更多还原

【Abstract】 A mathematical model for environmental ecosystem with impulsive control is presented.The(model) considers the effect of the same toxicant emitted into the closed polluted environment from external sources on two competing biological species,the uptake of toxicant by the competitors,and the pollution due to the competitors excrement reentering into the environment.The case of constant emission of the toxicant which only affects the birth rate of two biological species is emphasized.By using the method of linear approximation for impulsive systems with equidistant moment of impulsive effect,a sufficient condition which guarantees the model to be asymptotically stable at its unstable equilibrium point are obtained and the ecological explanation is also given.更多还原