|
| << vorige | volgende >> |
Tijdschrift beschrijving
Alle jaargangen van het bijbehorende tijdschrift
Alle afleveringen van het bijbehorende jaargang
Alle artikelen van de bijbehorende aflevering
Details van artikel 4 van 10 gevonden artikelen
| Titel: |
Dynamic reduction with applications to mathematical biology and other areas |
| Auteur: |
Sacker, Robert J. Von Bremen, Hubertus F. |
| Verschenen in: |
Journal of biological dynamics |
| Paginering: | Jaargang 1 (2007) nr. 4 pagina's 437-453 |
| Jaar: |
2007-10 |
| Inhoud: |
In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (1) alter that dependency by replacing part of the state variable by a function from a class having some of the above properties and (2) solve the 'reduced' equation for a solution having the remaining properties and lying in the same class. This then sets up a mapping T of the class into itself, thus reducing the original problem to one of finding a fixed point of the mapping. The procedure is applied to obtain a globally asymptotically stable periodic solution for a system of difference equations modeling the interaction of wild and genetically altered mosquitoes in an environment yielding periodic parameters. It is also shown that certain coupled periodic systems of difference equations may be completely decoupled so that the mapping T is established by solving a set of scalar equations. Periodic difference equations of extended Ricker type and also rational difference equations with a finite number of delays are also considered by reducing them to equations without delays but with a larger period. Conditions are given guaranteeing the existence and global asymptotic stability of periodic solutions. |
| Uitgever: |
Taylor & Francis |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 4 van 10 gevonden artikelen
| << vorige | volgende >> |