Abstract
A system of impulsive differential equations describing predator-prey dynamics with impulsive effect is proposed and analyzed with the assumption that a transmissible disease is spreading among the prey species only. At first, the “semi-trivial” periodic solution (S(t),0,0) is given. After that, the existence of “infection-free” periodic solution and the “predator-free” periodic solution (S(t),0, P(t)) have been obtained via bifurcation. Finally, the method of coincidence degree has been used to derive a set of sufficient conditions for the existence of at least one strictly positive periodic solution. Numerical simulations and a brief discussion conclude the paper.
Original language | English |
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Pages (from-to) | 3098-3111 |
Journal | Nonlinear Analysis: Real World Applications |
Volume | 10 |
Issue number | 5 |
Early online date | 18 Oct 2008 |
DOIs | |
Publication status | Published - 1 Oct 2009 |