NBT · Nonautonomous Bifurcation Theory
7РП — „Хора“ (Действия „Мария Кюри“)
- Период
- 2008-10-01 → 2010-09-30
- Финансиране от ЕС
- 160 659 €
- Участници
- 1
- Схема
- MC-IEF
Линиите свързват координатора с партньорите.
Накратко на български
Теорията на бифуркациите при неавтономни системи анализира как промените във времето или случайни влияния влияят върху динамиката на обекти като махало или кораб. Това помага за по-точното описание на поведението на сложни системи, които се променят постоянно.
Кратко обяснение, генерирано от езиков модел по текста на CORDIS. Оригиналът е по-долу.
Резултати накратко
Nonautonomous bifurcation theory
The central goal of this research project is the development of the bifurcation theory of nonautonomous (i.e., time-dependent, random or control) systems beyond the traditional setting. The following main objectives have been set up: (1) Characterization of bifurcations of low-dimensional nonautonomous dynamical systems. (2) Study of higher-dimensional bifurcation scenarios. (3) Development of a bifurcation theory for random systems with bounded noise. (4) Development of a concept of topological equivalence for nonautonomous dynamical systems; application to nonautonomous normal form theory. The following main results have been achieved: (1) Classification of bifurcations in one-dimensional nonautonomous differential equations: analogues of the classical bifurcation patterns. (2) Development of a numerical scheme to detect controlled heteroclinic orbits; application to a model for ship roll-motion, and to a pendulum coupled to an oscillator. (3) Development of a concept of exponential attractivity and bifurcation for finite-time systems; application to characterization the corresponding domain of attractions via an analogue of Borg's criterion. (4) Characterization of the almost periodicity of variational equations of almost periodic equations. (5) Characterization of discontinuous bifurcations in random systems systems with bounded noise as a collision process of attractors and repellers. (6) Development of a numerical scheme to approximate invariant sets in random systems with bounded noise; application to the perturbed Henon map. (7) Development of a concept of topological equivalence for nonautonomous differential equations; extension of conjugacies in the vicinity of hyperbolic solutions to global conjugacies.
Текст от CORDIS, на английски · Данни: CORDIS, © Европейски съюз
Цел на проекта
The mathematical concept of a dynamical system is founded on the fact that motions of many application processes are subjected to certain rules. Simple movements of a pendulum, complicated physical phenomena, chemical reactions, biological interactions (e.g., in predator-prey models) or even sociological patterns can be described via dynamical systems. Both the direct applicability of dynamical systems in numerous situations of the real life and the creation of the chaos theory in the 1960s have provided a great impetus to the theory of dynamical systems in the last decades and were a main reason for its success and popularity. For modeling real world phenomena, however, it is often inevitable to assume that the underlying rules are time-dependent, and the notion of a dynamical system is extended to this situation by the concept of a nonautonomous dynamical system. Nonautonomous situations arise quite frequently in the applied sciences, for instance, in studies of pollution spreading processes in coastal environments and climate modeling. In general, dynamical systems depend on parameters which reflect conditions influencing the system. In the dynamical bifurcation theory, the qualitative behaviour of the system under variation of these parameters is discussed. Although, the bifurcation theory for autonomous dynamical systems is a major object of research in the study of dynamical systems since decades, a corresponding theory for nonautonomous systems is still in its infancy, but in the last ten years, many renowned scientists started to think about nonautonomous bifurcation problems. The research and training project at hand aims at making major progress in the development of the nonautonomous bifurcation theory. In particular, further bifurcation patterns for low-dimensional systems are to be found, and moreover, high-dimensional systems shall be examined via reduction principles.
Оригинален текст от CORDIS (на английски).
Участници
- IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE · LondonКоординаторОбединеното кралство
Връзки
Данни: CORDIS, © Европейски съюз