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Dynamic behaviors of a single-species population model with birth pulses in a polluted environment. (English) Zbl 1178.34051

The authors consider the following system with impulses:

dx(t) dt=-rc(t)x(t)-dx(t),dc(t) dt=kf(t)-gc(t),df(t) dt=-hf(t)·

This system describes the dynamics of a single-species model with birth pulses, pulse harvesting and pulse toxicant input in a polluted environment.

Using a discrete dynamical system determined by the stroboscopic map, they obtain an exact 1-periodic solution of system whose birth function is the Ricker function or Beverton-Holt function, and obtain the threshold conditions for their stability.

MSC:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34A37Differential equations with impulses
34C25Periodic solutions of ODE