An impulsively controlled pest management model with n predator species and a common prey

• Published in: BioSystems Vol. 110; no. 3; pp. 162 - 170
• Main Authors: Georgescu, Paul, Zhang, Hong
• Format: Journal Article
• Language: English
• Published: Ireland Elsevier Ireland Ltd 01.12.2012
• Subjects: Animals; birth rate; Comparison estimates; Ecosystem; extinction; Floquet theory; Impulsive controls; Integrated pest management; Models, Biological; mortality; Permanence; Pest Control - statistics & numerical data; Pest Control, Biological - statistics & numerical data; Population Dynamics; predation; predator-prey relationships; predators; Predatory Behavior; Stability; Comparison estimates; 34A37; 34D23; Stability; 92D25; Impulsive controls; Floquet theory; Permanence; Integrated pest management
• ISSN: 0303-2647; 1872-8324; 1872-8324
• DOI: 10.1016/j.biosystems.2012.10.001

This paper investigates the dynamics of a competitive single-prey n-predators model of integrated pest management, which is subject to periodic and impulsive controls, from the viewpoint of finding sufficient conditions for the extinction of prey and for prey and predator permanence. The per capita death rates of prey due to predation are given in abstract, unspecified forms, which encompass large classes of death rates arising from usual predator functional responses, both prey-dependent and predator-dependent. The stability and permanence conditions are then expressed as balance conditions between the cumulative death rate of prey in a period, due to predation from all predator species and to the use of control, and to the cumulative birth rate of prey in the same amount of time. These results are then specialized for the case of prey-dependent functional responses, their biological significance being also discussed.