The dynamic properties of a crop-pest-natural enemy model with group defense behavior are stud-ied.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 analy-sis results are validated through numerical simulations.
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