Applications Of Impulse In Biological Invasion Population Model

This paper mainly studies three types of models: an infectious disease model of single specieswith impulse at fixed times, a predator-prey model with impulse at fixed times, and a predator-preymodel with state impulse and with Beddington-DeAnglis functional response. For the infectiousdisease model of single species, the paper obtains the boundedness of solutions with positive initialconditions, and also some sufficient extinction conditions and persistence conditions by using thecomparison theorem in impulsive differential equations and Floquent theory. For the predator-preymodel of two species with time-delay and impulse at fixed times, the paper obtains the boundednessof solutions, the persistence conditions of the subsystem, and the local asymptotic stability conditionsof periodic solutions; for the predator-prey model of three species with impulse at fixed times, thepaper numerically simulates the solutions and confirms the influence of impulse period on the system.Finally, assuming that the choice of impulsive time depends on the population, the paper proposes apredator-prey model of state impulse with functional response of Beddington-DeAnglis type andobtains the existence and stability conditions of periodic solutions of order1by constructing thePoincare mapping and the phase portrait of the system. Numeric simulations are applied to all threetypes of models, which support the theoretical results.