Transcritical bifurcation yielding global stability for network processes. (English) Zbl 1441.34070
In this paper, the dynamical system
\[
\dot x(t)=f(x(t)) \tag{1}
\]
is considered in the unit cube \(Q=\{x\in \mathbb{R}^n: 0\le x_i\le 1, i=1,\dots,n\}\) where \(f:\mathbb{R}^n\to\mathbb{R}^n\) is a differentiable function. If \(x=0\) is a solution of system (1),
the authors specify sufficient conditions of its global asymptotic stability.
Reviewer: Alexander O. Ignatyev (Donetsk)
MSC:
| 34D23 | Global stability of solutions to ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
Keywords:
global asymptotic stabilityReferences:
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