一类具有群体防御行为的庄稼-害虫-天敌模型的动力学分析

Research on the Dynamics of a Crop-pest-natural EnemyModel with Group Defense Behavior

研究一类具有群体防御行为的庄稼-害虫-天敌模型的动力学性质.首先,给出了正平衡点的存在条件以及平衡点局部渐近稳定的条件;其次,利用规范型理论和中心流型定理系统分析了Hopf分支的相关性质,包括存在性、稳定性和分支方向等;最后,通过数值模拟验证理论分析的结果.

The dynamic properties of a crop-pest-natural enemy model with group defense behavior are studied.Firstly,the conditions for the existence of equilibria and the local asymptotic stability of the equilibria are determined.Next,the properties of Hopf bifurcation,such as existence,stability,and bifurcation direction,are systematically analyzed by using normal form theory and center manifold theorem.Finally,the theoretical analysis results are validated through numerical simulations.