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Central Manifold for ordinary differential equations
- Speaker(s)
- Marek Bodnar
- Affiliation
- MIM
- Language of the talk
- English
- Date
- Jan. 7, 2026, 2:15 p.m.
- Room
- room 5070
- Seminar
- Seminar of Biomathematics and Game Theory Group
The Centre Manifold Theorem provides a powerful framework for analysing dynamical systems with equilibria for which linearisation is inconclusive due to the presence of eigenvalues with zero real parts. By reducing the dynamics to an invariant centre manifold, the local behaviour of the full system can be described by a lower-dimensional equation.
In this talk, we present the existence and basic properties of local centre manifolds, together with the Reduction Principle, which links the stability of an equilibrium to the dynamics on the centre manifold. An approximation theorem is discussed as a practical tool for computing centre manifolds near equilibria. Several examples, including applications motivated by biological models, illustrate how centre manifold techniques can be used to determine stability and asymptotic behaviour in nonlinear systems.
