Publication details
Asymptotic properties of a two-dimensional differential system with delay
| Authors | |
|---|---|
| Year of publication | 2007 |
| Type | Article in Proceedings |
| Conference | Proceedings of Equadif-11 |
| MU Faculty or unit | |
| Citation | |
| Field | General mathematics |
| Keywords | Delayed differential equations; asymptotic behaviour; stability; boundedness of solutions; two-dimensional systems; Lyapunov method; Wazewski topological principle. |
| Description | The asymptotic nature of the solutions of a real two-dimensional system of retarded differential equations x'(t) = A(t)x(t) + B(t)x(t-r)+ h(t,x(t),x(t-r)), where r>0 is a constant delay, A, B and h being matrix functions and a vector function, respectively, is examined. The method of complexification transforms this system to one equation with complex-valued coefficients. Stability and the asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle. |
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