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Bifurcation of nontrivial periodic solutions for an impulsively controlled pest management model. (English) Zbl 1151.34037

Summary: This paper investigates the onset of nontrivial periodic solutions for an integrated pest management model which is subject to pulsed biological and chemical controls. The biological control consists in the periodic release of infective individuals, while the chemical control consists in periodic pesticide spraying. It is assumed that both controls are used with the same periodicity, although not simultaneously. To model the spread of the disease which is propagated through the release of infective individuals, an unspecified force of infection is employed.

The problem of finding nontrivial periodic solutions is reduced to showing the existence of nontrivial fixed points for the associated stroboscopic mapping of time snapshot equal to the common period of controls. The latter problem is in turn treated via a projection method. It is then shown that once a threshold condition is reached, a stable nontrivial periodic solution emerges via a supercritical bifurcation.

34C60Qualitative investigation and simulation of models (ODE)
34A37Differential equations with impulses
92D25Population dynamics (general)
34C23Bifurcation (ODE)
37G15Bifurcations of limit cycles and periodic orbits
34H05ODE in connection with control problems
34C25Periodic solutions of ODE