Asymptotic properties of a two-dimensional differential system with a bounded nonconstant delay under the conditions of instability
| Authors | |
|---|---|
| Year of publication | 2008 |
| Type | Article in Periodical |
| Magazine / Source | Far East Journal of Mathematical Sciences |
| MU Faculty or unit | |
| Citation | |
| Web | http://pphmj.com/journals/articles/423.htm |
| Field | General mathematics |
| Keywords | Delayed differential equations - Asymptotic behaviour - Boundedness of solutions - Lyapunov method - Wazewski topological principle |
| Description | In this paper, the asymptotic behaviour for the solutions of a real two-dimensional system with a nonconstant delay is studied under the assumption of instability. The conditions for the instable properties of solutions together with the conditions for the the existence of bounded solutions or solutions tending to the origin are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle. The results generalize some previous results, where the asymptotic properties for two-dimensional systems with a constant delay were studied. |
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