American Institute of Mathematical Sciences

Advanced
2005, 2(2): 329-344. doi: 10.3934/mbe.2005.2.329

Impulsive Ecological Control Of A Stage-Structured Pest Management System

Guirong Jiang 1, , Qishao Lu 2, and  Linping Peng 2,

1. 

Department of Computational Science and Mathematics, Guilin University of Electronic Technology, Guilin 541004, China
2. 

School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China

Received  July 2004 Revised  March 2005 Published  March 2005

The dynamics of a stage-structured pest management system is studied by means of autonomous piecewise linear systems with impulses governed by state feedback control. The sufficient conditions of existence and stability of periodic solutions are obtained by means of the sequence convergence rule and the analogue of the Poincaré criterion. The attractive region of periodic solutions is investigated theoretically by qualitative analysis. The bifurcation diagrams of periodic solutions are obtained by using the Poincaré map, as well as the chaotic solution generated via a cascade of period-doubling bifurcations. The superiority of the state feedback control strategy is also discussed.
Keywords: bifurcation., autonomous systems with impulses, prey-predator.
Mathematics Subject Classification: 34A37, 92D2.
Citation: Guirong Jiang, Qishao Lu, Linping Peng. Impulsive Ecological Control Of A Stage-Structured Pest Management System. Mathematical Biosciences & Engineering, 2005, 2 (2) : 329-344. doi: 10.3934/mbe.2005.2.329
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