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In this paper, we introduce a class of predator–prey system with general functional response, whose harvesting policy is modeled by a discontinuous function. Based on the differential inclusions theory, topological degree theory in set‐valued analysis and generalized Lyapunov approach, we analyze the existence, uniqueness and global asymptotic stability of positive periodic solution. In particular, a series of useful criteria on existence, uniqueness and global asymptotic stability of the positive equilibrium point are established for the autonomous system corresponding to the non‐autonomous biological and mathematical model with a discontinuous right‐hand side. Moreover, some new sufficient conditions are provided to guarantee the global convergence in measure of harvesting solution and convergence in finite time of any positive solution for the autonomous discontinuous biological system. The obtained results, which improve and generalize previous works on dynamical behavior in the literature, are of interest for understanding and designing biological system with not only continuous or even Lipschitz continuous but also discontinuous harvesting function. Finally, we give three examples with numerical simulations to show the applicability and effectiveness of our main results. Copyright © 2015 John Wiley & Sons, Ltd.  相似文献
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通过考虑需求函数和供给函数受到不连续因素的影响以及引进切换型的控制策略,建立由右端不连续微分方程刻画的非线性价格调整模型.利用微分包含理论和Lyapunov稳定性方法分析不连续价格调整模型的有限时间稳定化控制问题,并给出数值模拟实例进行验证说明.最后,结合动态经济学数学建模提出数学建模教学改革的几点建议.  相似文献
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