Center manifold analysis and scaling in population biology

Venue: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Sala Seminari "-1"
At: 11 am

Speaker:

• Nico Stollenwerk (University of Lisbon)

Abstract:

The center manifold analysis is presented as a method of time scale separation, applied to population biological models, especially in epidemiology. The spectral gap of the eigenvalues of the Jacobian matrix around the non-trivial stationary state gives the time scale separation. In previous work (Rocha et al., 2013) we analyzed the center manifold to zero'th order in the scaling parameter. Here higher orders in the scaling parameter are discussed. After the simplest two dimensional models with all steps performed analytically, the extension to higher dimensional models is shown, where the dimensionality of fast and slow time scales follows from the eigenvalue spectral gap around the considered stationary state. This can be generalized to any attractor, not only fixed points. Especially for chaotic attractors the Lyapunov spectrum gives the information of spectral gaps. Finally, a comparison of the center manifold analysis with singular perturbation is discussed, and applications to multi-strain epidemiological model with positive Lyapunov exponents outlined (with examples from dengue fever epidemiology).

Contact person: Maira Aguiar