Abstract
A two species commensal symbiosis model with non-monotonic functional response takes the form $$ \di\frac{dx}{dt}=x\Big(a_1-b_1x+\di\frac{c_1y }{d_1+y^2}\Big), \di\frac{dy}{dt}=y(a_2-b_2y) $$ is proposed and studied, where $a_i, b_i, i=1,2$ $c_1$ and $d_1$ are all positive constants. We show that the system admits a unique globally asymptotically stable positive equilibrium. https://doi.org/10.28919/cmbn/2839
Highlights
We show that the system admits a unique globally asymptotically stable positive equilibrium
The aim of this paper is to investigate the dynamic behaviors of the following two species commensal symbiosis model with non-monotonic functional response dx dt c1y d1 + y2
3, we will investigate the global stability property of the positive equilibrium; In Section 4, an example together with its numeric simulation is presented to show the feasibility of our main results
Summary
Sun and Wei[11] first time proposed a intraspecific commensal model: dx dt r1x k1 − x + ay k1 They investigated the local stability of all equilibrium points. Xie et al [13] proposed the following discrete commensal symbiosis model x1(k + 1) = x1(k) exp a1(k) − b1(k)x1(k) + c1(k)x2(k) , x2(k + 1) = x2(k) exp a2(k) − b2(k)x2(k) , They showed that the system (1.4) admits at least one positive ω-periodic solution. It brings to our attention that all of the above works are based on the traditional Lotka-Volterra model, which suppose that the influence of the second species to the first one is linearize This may not be suitable since the commensal between two species become infinity as the density of the species become infinity. 3, we will investigate the global stability property of the positive equilibrium; In Section 4, an example together with its numeric simulation is presented to show the feasibility of our main results
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