Publication Type

Journal Article

Journal Name

Modeling and Simulation in Science, Engineering and Technology

Publication Date

1-1-2008

Abstract

This chapter is devoted to the analysis of single-species population dynamics models with overlapping and non-overlapping generations. Within the framework of all models it is assumed that there are no activities of individuals during the wintertime (as, for example, is the case for forest insect populations in the boreal zone), and changes in population size at these moments are described with a broken trajectory (“jump down”). Also, it is assumed that the fecundity of individuals is constant and that the quota of individuals surviving winter depends on the within-year population dynamics. The dynamics of the models, which are determined by the influence of winter conditions on the survival of individuals and by the influence of intrapopulation self-regulative mechanisms, are analyzed. For some particular cases the conditions for population extinction and for stabilization at a non-zero level are determined; it is shown numerically that chaotic regimes can also be realized in some models. The conditions for the reduction of the models under consideration to some well-known discrete models are obtained.

Keywords

discrete models, ordinary differential equations with impulses, Population dynamics

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