A pest control model with state-dependent impulses

In this paper, a pest control model with state-dependent impulses is firstly established, which relies on releasing of natural enemies, together with spraying pesticides. By using the successor function of differential equation geometry rules, the existence of order one periodic solution is discussed. According to the Analogue of Poincare's Criterion, the orbitally asymptotic stability of the order one periodic solution is obtained. Furthermore, we investigated the global attractor of the system. From a biological point of view, our results indicate that: (1) the pest population can be controlled below some threshold; (2) compared to single measure, it is more efficient to take two measures for reducing the level of the pests.

[1]  P. S. Simeonov,et al.  Orbital stability of periodic solutions of autonomous systems with impulse effect , 1988 .

[2]  N. Scopes,et al.  Biological control by predatory mites (Phytoseiulus persimilis Athias-Henriot) of red spider mite (Tetranychus urticae Koch) infesting strawberries grown in walk-in' plastic tunnels , 1981 .

[3]  L. Beaumont,et al.  Predicting species distributions: use of climatic parameters in BIOCLIM and its impact on predictions of species’ current and future distributions , 2005 .

[4]  Qingling Zhang,et al.  The geometrical analysis of a predator-prey model with two state impulses. , 2012, Mathematical biosciences.

[5]  Eizi Yano,et al.  Predation by Orius sauteri (Poppius) (Heteroptera: Anthocoridae) on Thrips palmi Karny (Thysanoptera: Thripidae): Functional response and selective predation , 2000 .

[6]  Guirong Jiang,et al.  Impulsive ecological control of a stage-structured pest management system. , 2005, Mathematical biosciences and engineering : MBE.

[7]  Min Zhao,et al.  HOMOCLINIC BIFURCATION IN SEMI-CONTINUOUS DYNAMIC SYSTEMS , 2012 .

[8]  Ruiqing Shi,et al.  A predator-prey model with disease in the prey and two impulses for integrated pest management , 2009 .

[9]  Bing Liu,et al.  DYNAMICS ON A HOLLING II PREDATOR–PREY MODEL WITH STATE-DEPENDENT IMPULSIVE CONTROL , 2012 .

[10]  Antoine Guisan,et al.  Predictive habitat distribution models in ecology , 2000 .

[11]  J. Logan,et al.  Temperature-dependent phenology and predation in arthropod systems , 2006 .

[12]  Chunjin Wei,et al.  HETEROCLINIC BIFURCATIONS OF A PREY–PREDATOR FISHERY MODEL WITH IMPULSIVE HARVESTING , 2013 .

[13]  S. Chander,et al.  InfoCrop: A dynamic simulation model for the assessment of crop yields, losses due to pests, and environmental impact of agro-ecosystems in tropical environments. I. Model description , 2006 .

[14]  M. J. Salinger,et al.  Reducing Vulnerability of Agriculture and Forestry to Climate Variability and Change: Workshop Summary and Recommendations , 2005 .

[15]  Sanyi Tang,et al.  State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences , 2005, Journal of mathematical biology.

[16]  Yongzhen Pei,et al.  Pest regulation by means of continuous and impulsive nonlinear controls , 2010, Math. Comput. Model..