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Zbl 1178.34051
Tao, Fengmei; Liu, Bing
Dynamic behaviors of a single-species population model with birth pulses in a polluted environment. (English)
[J] Rocky Mt. J. Math. 38, No. 5, 1663-1684 (2008). ISSN 0035-7596

The authors consider the following system with impulses: $$\align \frac{dx(t)}{dt} &=-rc(t)x(t)-dx(t), \\ \frac{dc(t)}{dt}&=kf(t)-gc(t), \\ \frac{df(t)}{dt}&=-hf(t). \endalign$$ 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.
[Leonid Berezanski (Beer-Sheva)]

MSC 2000:: *34C60 Applications of qualitative theory of ODE
92D25 Population dynamics
34A37 Differential equations with impulses
34C25 Periodic solutions of ODE

Keywords: single-species population model; impulses; dynamic behavior; periodic solutions

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Zentralblatt MATH Berlin [Germany]