Liang Zhao, Runxin Wu, Permanence of a nonlinear competition model with delay, Vol. 2017 (2017), Article ID 11, pp. 1-11

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DOI: 10.23952/cot.2017.11

Received June 15, 2016; Accepted December 3, 2016; Published January 10, 2017

Abstract. Sufficient conditions are obtained for the permanence of the following nonlinear competition model $\frac{dN_1(t)}{dt}=$ $r_1(t)N_1(t)$ $[\frac{K_1(t)+\alpha_1(t)N_2^{\beta_{12}}(t-\tau_2(t))}{1+N_2^{\beta_{12}}(t-\tau_2(t))}-N_1^{\beta_{11}}(t-\sigma_1(t))],$ $\frac{dN_2(t)}{dt}=$ $r_2(t)N_2(t)$ $[\dfrac{K_2(t)+\alpha_2(t)N_1^{\beta_{21}}(t-\tau_1(t))}{1+N_1^{\beta_{21}}(t-\tau_1(t))}-N_2^{\beta_{22}}(t-\sigma_2(t))],$ where $r_i,$ $K_i, \alpha_i$ , $\tau_i$ and $\sigma_i, i=1,2$ are continuous functions bounded above and below by positive constants, $K_i>\alpha_i, i=1,2,$ $\beta_{ij}, i, j=1, 2$ are all positive constants.

How to Cite this Article:

Liang Zhao, Runxin Wu, Permanence of a nonlinear competition model with delay, Communications in Optimization Theory, Vol. 2017 (2017), Article ID 11, pp. 1-11.