CAJ | 학술논문

从生物动力学的角度扩展了传统的Lotka-Voltera捕食-被捕食模型,以Holling-II型和修改的Leslie-Gower型功能反应为基础,建立了包括密度制约、功能反应和时滞效应的二维非线性时滞动力系统模型;分析了该动力系统的持久性、稳定性及时滞效应对系统动力学性质的影响;证明了系统在一定的条件下是一致持久的;通过构造适当的Lyapunov函数,得到了系统的正平衡点全局渐近稳定性的充分条件;讨论了诸时滞参数值变化对系统正平衡点稳定性的影响.
종생물동역학적각도확전료전통적Lotka-Voltera포식-피포식모형,이Holling-II형화수개적Leslie-Gower형공능반응위기출,건립료포괄밀도제약、공능반응화시체효응적이유비선성시체동력계통모형;분석료해동력계통적지구성、은정성급시체효응대계통동역학성질적영향;증명료계통재일정적조건하시일치지구적;통과구조괄당적Lyapunov함수,득도료계통적정평형점전국점근은정성적충분조건;토론료제시체삼수치변화대계통정평형점은정성적영향.
By extending the conventional Lotka-Volterra model of predator-prey from the viewpoint of biomechanics,the new dynamical model of two-dimensional nonlinear time-delayed differential equation is established,which is based on Holling-type II and Leslie-Gower modified functional response and includes the carrying capacity of the environmental resources and functional response.Its persistence and its equilibrium point's stability and the effect of delayed times on its dynamics is analyzed.The system is uniformly persistent under some appropriate conditions.A sufficient condition for global stability of the positive equilibrium point is obtained by constructing a proper Lyapunov function.Finally the effect of changing time-delayed parametric value on its stability is discussed.