Asymptotic behaviour of a two-dimensional differential system with a nonconstant delay under the conditions of instability
| Authors | |
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| Year of publication | 2011 |
| Type | Article in Periodical |
| Magazine / Source | Mathematica Bohemica |
| MU Faculty or unit | |
| Citation | |
| Web | Mathematica Bohemica |
| Field | General mathematics |
| Keywords | delayed differential equations; asymptotic behaviour; boundedness of solutions; Lyapunov method; Wazewski topological principle |
| Description | Several results dealing with the asymptotic behaviour of a real nonlinear two-dimensional system with a finite number of bounded nonconstant delays under the assumption of instability are presented. Conditions for the instable properties of solutions together with the conditions for the existence of bounded solutions are given. The methods are based on the transformation of the real system considered to one equation with complex-valued coefficients. Asymptotic properties are studied by means of a suitable Lyapunov-Krasovskii functional and the Wazewski topological principle. The results generalize some previous ones, where the asymptotic properties for two-dimensional systems with one constant or nonconstant delay were studied. |
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