## Ultimate boundedness for nonautonomous diffusive Lotka-Volterra patches.(English)Zbl 0663.92016

The asymptotic behavior of n biological species living in two patches is investigated. The governing mathematical model reads as a system of ordinary differential equations of the form $\dot x_ i=x_ i[e_ x(t)+A_ x(t)x]_ i+D_ i(t)(y_ i-x_ i),\quad \dot y_ i=y_ i[e_ y(t)+A_ y(t)y]_ i+D_ i(t)(x_ i-y_ i),$ i$$=1,2,...,n$$, where $$e_ x,e_ y: {\mathbb{R}}\to {\mathbb{R}}^ n$$, $$A_ x,A_ y: {\mathbb{R}}\to R^{n\times n}$$, $$x=col(x_ 1,x_ 2,..,x_ n)$$, $$y=col(y_ 1,y_ 2,...,y_ n)$$. Sufficient conditions which guarantee the ultimate boundedness property of the (positive) solutions are given.
Reviewer: G.Karakostas

### MSC:

 92D40 Ecology 34D40 Ultimate boundedness (MSC2000)
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### References:

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