Non-smooth Filippov Stage-structured Pest Growth Models

In a natural world, the pest’s diversities consist of populations of individuals of different ages, sizes, or life stages and those diversities have a significant influence upon dynamics at the population level and successful pest control. The stage-structured population models have received much attraction and been proposed to the pest control strategies by many scientists. It is well known that the integrated pest management(IPM) strategies are effective and reliable tactic to control the pest population such that its density does not exceed the economic injury level, which is cost effective and can decrease the effects of pesticides on environment. In order to control the pest population such that its density does not exceed the economic injury level, we have developed the non-smooth two-stage structured pest growth model using threshold policy control strategy.The basic two-stage structured pest growth model employed in this thesis is where x, y represent the juvenile populations and the adult populations, b is the per capita juvenile population birth rate, bexp[-(ax+y)]y in the model indicate that a strong effect on the per capita birth rate by intra-adult competition occurs, c is the transformation rate of the juvenile population to the adult population, δ1and δ2are the death rates of the juvenile population and the adult population, respectively. Choosing the density of the juveniles as the index, we implement the control strategy once the density of juvenile populations increases and exceeds the economic threshold (ET). Therefore, if I> ET, then both juvenile and adult populations follow the following equation: where q1and q2are killing rates, and if I<ET then both juvenile and adult populations follow the model (1). Consequently, the models (1) and (2) can be rewritten as the following Filippov system withFor this non-smooth dynamical system, the sliding mode domain, sliding mode dynamics and existence of equilibria including regular, virtual and pseudo-equilibria have been addressed in this thesis. Further, the stability of those equilibria are investigated by employing theoretical and numerical methods. By employing the analytical techniques of non-smooth dynamic system, the local sliding bifurcations including boundary node (saddle), tangency, pseudo-saddle-node bifurcations are addressed. The biological implications related to pest control are also discussed, and our results indicates that the number of juvenile populations can be successfully maintained below the ET by designing suitable threshold policy strategy.