Abstract
This paper investigates stability conditions and positivity of the solutions of a coupled set of nonlinear difference equations under very generic conditions of the nonlinear real functions which are assumed to be bounded from below and nondecreasing. Furthermore, they are assumed to be linearly upper bounded for sufficiently large values of their arguments. These hypotheses have been stated in 2007 to study the conditions permanence.
Highlights
There is a wide scientific literature devoted to investigate the properties of the solutions of nonlinear difference equations of several types 1–9
The above difference system is very useful for modeling discrete neural networks which are very useful to describe certain engineering, computation, economics, robotics, and biological processes of populations evolution or genetics 1
The study in 1 about the permanence of the above system is performed under very generic conditions on the functions fi : R → R, for all i ∈ k
Summary
There is a wide scientific literature devoted to investigate the properties of the solutions of nonlinear difference equations of several types 1–9. Other equations of increasing interest are as follows:. The stability, positivity, and permanence of such equations are of increasing interest. The following system of difference equations is considered 1 : xni 1 λixni fi αixni 1 − βixni−11 , ∀i ∈ k : {1, 2, . Xnk T ∈ Rk, for all n ∈ N, under initial conditions xj : xj[1 ], xj2 , . The study in 1 about the permanence of the above system is performed under very generic conditions on the functions fi : R → R, for all i ∈ k. General conditions for the global stability and positivity of the solutions are investigated
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