Dynamic behaviors of a single-species population model with birth pulses in a polluted environment (Q1011091)

The authors consider the following system with impulses: \[ \begin{aligned} \frac{dx(t)}{dt} &=-rc(t)x(t)-dx(t), \\ \frac{dc(t)}{dt}&=kf(t)-gc(t), \\ \frac{df(t)}{dt}&=-hf(t). \end{aligned} \] 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.