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Zbl 1187.34050
Hu, Daowei; Zhang, Zhengqiu
Four positive periodic solutions to a Lotka-Volterra cooperative system with harvesting terms. (English)
[J] Nonlinear Anal., Real World Appl. 11, No. 2, 1115-1121 (2010). ISSN 1468-1218

Summary: We consider the following Lotka-Volterra cooperative system with harvesting terms: $$\cases x'(t)=x(t)(a_1(t)-b_1(t)x(t)+c_1(t)y(t))-h_1(t),\\ y'(t)=y(t)a_2(t)-b_2(t)y(t)+c_2(t)x(t))-h_2(t),\endcases\tag1$$ where $x(t)$ and $y(t)$ denote the densities of two cooperative species, respectively: $a_i(t), b_i(t), c_i(t)$ and $h_i(t)$ $(i=1,2)$ are all positive continuous functions denoting the intrinsic growth rate, death rate, cooperative rate between the two species, harvesting rate, respectively. We establish the existence of four positive periodic solutions of (1) by using the continuation theorem of coincidence degree.

MSC 2000:: *34C25 Periodic solutions of ODE
92D25 Population dynamics
47N20 Appl. of operator theory to differential and integral equations

Keywords: four positive periodic solutions; Lotka-Volterra cooperative system; continuation theorem of coincidence degree theory; harvesting term

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