| Autor: |
Avitabile, Daniele, Desroches, Mathieu, Veltz, Romain, Wechselberger, Martin |
| Rok vydání: |
2019 |
| Předmět: |
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| Zdroj: |
SIAM Journal on Mathematical Analysis, 2020, 52(6), 5703-5747 |
| Druh dokumentu: |
Working Paper |
| DOI: |
10.1137/19M1306610 |
| Popis: |
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an infinite-dimensional dynamical system for the fast variables is coupled to a finite-dimensional dynamical system for slow variables. We prove the existence of centre-manifolds for generic models of this type, and study the reduced, finite-dimensional dynamics near bifurcations of (possibly) patterned steady states in the layer problem. Theoretical results are complemented with detailed examples and numerical simulations covering systems of local- and nonlocal-reaction diffusion equations, neural field models, and delay-differential equations. We provide analytical foundations for numerical observations recently reported in literature, such as spatio-temporal canards and slow-passages through Hopf bifurcations in spatially-extended systems subject to slow parameter variations. We also provide a theoretical analysis of slow passage through a Turing bifurcation in local and nonlocal models. |
| Databáze: |
arXiv |
| Externí odkaz: |
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