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Zbl 1151.34037
Georgescu, Paul; Zhang, Hong; Chen, Lansun
Bifurcation of nontrivial periodic solutions for an impulsively controlled pest management model. (English)
[J] Appl. Math. Comput. 202, No. 2, 675-687 (2008). ISSN 0096-3003

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.
MSC 2000:
*34C60 Applications of qualitative theory of ODE
34A37 Differential equations with impulses
92D25 Population dynamics
34C23 Bifurcation (periodic solutions)
37G15 Bifurcations of limit cycles and periodic orbits
34H05 ODE in connection with control problems
34C25 Periodic solutions of ODE

Keywords: nontrivial periodic solutions; bifurcation; impulsive controls; nonlinear force of infection; fixed point argument

Cited in: Zbl 1179.37071

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