A Volterra model with mutual interference
concerning integrated pest management is proposed and analyzed. By
using Floquet theorem and small amplitude perturbation method and
comparison theorem, we show the existence of a globally
asymptotically stable pest-eradication periodic solution. Further,
we prove that when the stability of pest-eradication periodic
solution is lost, the system is permanent and there exists a
locally stable positive periodic solution which arises from the
pest-eradication periodic solution by bifurcation theory. When the
unique positive periodic solution loses its stability, numerical
simulation shows there is a characteristic sequence of
bifurcations, leading to a chaotic dynamics. Finally, we compare
the validity of integrated pest management (IPM) strategy with
classical methods and conclude IPM strategy is more effective than
classical methods.