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QUALITATIVE THEORY AND NON-DEGENERATE AND DEGENERATE BIFURCATIONS IN n-DIMENSIONAL DYNAMICAL SYSTEMS

Objectif

Dynamical systems theory contains important tools in investigating various theoretical and practical models generated by systems of differential equations. Such models may be found in a lot of areas, ranging from Mathematics, Engineering to Medicine and Psychiatry. In this project we address some unexplored themes in this field. We will study degenerate codimension-2 bifurcations in n-dimensional dynamical systems. Of these bifurcations we will focus on the fold-Hopf degenerate bifurcation, firstly in three dimensional nonlinear continuous dynamical systems and then we will generalize it for n-dimensional dynamical systems. In discrete dynamical systems, an analogous of the continuous fold-Hopf bifurcation will also be addressed. The existence and number of limit cycles in two-dimensional (polynomial, Hamiltonian, perturbed Hamiltonian) continuous and discontinuous differential systems is another objective of this project. Using Melnikov functions of any order we will give new insights on the existence and number of limit cycles in these systems. Finally, we are interested in investigating some practical models.

Appel à propositions

FP7-PEOPLE-IEF-2008
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Coordinateur

IMPERIAL COLLEGE OF SCIENCE TECHNOLOGY AND MEDICINE
Adresse
South Kensington Campus Exhibition Road
SW7 2AZ London
United Kingdom
Type d’activité
Higher or Secondary Education Establishments
Contribution de l’UE
€ 231 036,29
Contact administratif
Brooke Alasya (Ms.)