About a dynamic model of interaction of insect population with food plant

Abstract

In present paper there is the consideration of mathematical model of food plant (resource) - consumer (insect population) - pathogen system dynamics which is constructed as a system of ordinary differential equations. The dynamic regimes of model are analyzed and, in particular, with the help of numerical methods it is shown that trigger regimes (regimes with two stable attractors) can be realized in model under very simple assumptions about ecological and intra-population processes functioning. Within the framework of model it was assumed that the rate of food flow into the system is constant and functioning of intra-population selfregulative mechanisms can be described by Verhulst model. As it was found, trigger regimes are different with respect to their properties: in particular, in model the trigger regimes with one of stable stationary points on the coordinate plane can be realized (it corresponds to the situation when sick individuals in population are absent and their appearance in small volume leads to their asymptotic elimination); also the regimes with several nonzero stationary states and stable periodic fluctuations were found.

Keywords

• population dynamics
• mathematical model
• trigger regimes
• insect population outbreak