A result on a feedback system of ordinary differential equations
This paper deals with a feedback system of ordinary differential equations of the form \(x_ 1'=f_ 1(x_ 1,x_ n)\), \(x_ i'=f_ i(x_{i-1},x_ i,x_{i+1})\) \((2\leq i\leq n-1)\), \(x_ n'=f_ n(x_{n- 1},x_ n)\) where \(f_ i(i=1,2,\dots,n)\) satisfy some monotonicity conditions. The main result concerns the asymptotic behavior of bounded solutions. More specifically it is shown that the \(\omega\)-limit of such a solution contains at least one rest point or periodic point. An example for the case of an interacted 4-species model with linear per capita growth rate illustrates the result.
feedback system of ordinary differential equations
scientific article; zbMATH DE number 94577