状态反馈脉冲控制的福寿螺-水稻防控数学模型

The Prevention and Control Mathematical Model for the Pomacea Canaliculata-Rice with Impulsive State Feedba

福寿螺作为入侵生物,已经在农业生产和生态环境等方面产生了一系列危害.建构一类具有状态脉冲反馈控制的福寿螺-水稻的生态系统,通过在田中放养鸭子,并结合脉冲喷洒天然植物制剂-茶麸水的方法,综合防治福寿螺.首先,运用稳定性理论得到无脉冲作用系统正平衡点的全局稳定性结论;其次,对具有状态反馈控制的脉冲系统,用微分方程几何理论和后继函数的方法得到系统阶1周期解的存在唯一性,并给出阶1周期解轨道渐近稳定的条件;最后,利用数值模拟验证主要结论.

The golden apple snail(Pomacea canaliculata),as a typical invading creature,has been influencing agricultural production and ecology.In this paper,the golden apple snail-rice system with mutual interference and impulsive state feedback control is constructed.A method that feed ducks in rice paddies by combining a natural plant preparation with tea bran is pulsed sprayed to control snails.Firstly,by using the stability theorem,we obtain the global asymptotic stability of the positive equilibrium for the system without impulse effects.Secondly,by using the geometric theory of differential equations,the method of successor functions and mathematical analysis,we obtain some sufficient conditions for the existence,uniqueness and orbital asymptotically stability of the order-1 periodic solution for the system with impulse effects.Finally,The mathematical results are verified by numerical simulations.