On The Dynamics Behavior Of Single-species Population Model With Stage Structure And Birth Pulses

Impulsive differential equations are suitable for the mathematical simulation of evolutionary processes which experience a change of state abruptly owing to instantaneous perturbations. In terms of the mathematical treatment, the presence of impulses gives the system a mixed nature, both continuous and discrete. The theory of impulsive differential equations is much richer than the corresponding theory of differential equations without impulsive effects. It is well-known that many real world phenomena and human activeties do exibit impulsive effects. In this thesis, based on impulsive differential equations, we establish and investigate the dynamical behaviors of a kind of a single species model with stage structure, birth pulse and seasonal harvesting. By using sto-boscopic map we explore the effects of birth pulse and harvest timing on the dynamical complexity. We obtain an exact 1-periodic solution of systems, which are with Ricker function and Beverton-Holt function and obtain the threshold conditions for their stability. By numerical simulations we find that the dynamical behaviors of the stage-structured population models with birth pulse and resonal havesting are very complex, including period-doubling cascade, period-halving cascade, chaotic bands with periodic windows and "period-adding" phenomena. Further, we show that the timing of harvesting has a strong impact on the management of pest population. We also give an specific example in fish harvest to interpret that resoning havesting has a strong impact on the persistence of fish population and on the maximum annual-sustainable...