Zobrazeno 1 - 10
of 71
pro vyhledávání: '"Martin Wechselberger"'
The Role of Cell Volume in the Dynamics of Seizure, Spreading Depression, and Anoxic Depolarization.
Publikováno v:
PLoS Computational Biology, Vol 11, Iss 8, p e1004414 (2015)
Cell volume changes are ubiquitous in normal and pathological activity of the brain. Nevertheless, we know little of how cell volume affects neuronal dynamics. We here performed the first detailed study of the effects of cell volume on neuronal dynam
Externí odkaz:
https://doaj.org/article/55f89beaf4db4ddba4b65aef28b65432
Publikováno v:
SIAM Journal on Applied Dynamical Systems. 21:982-1029
Phenomena in chemistry, biology and neuroscience are often modelled using ordinary differential equations (ODEs) in which the right-hand-side is comprised of terms which correspond to individual 'processes' or 'fluxes'. Frequently, these ODEs are cha
Publikováno v:
Journal of Nonlinear Science. 30:3161-3198
We develop the contact singularity theory for singularly perturbed (or ‘slow–fast’) vector fields of the general form $$z' = H(z,\varepsilon )$$ , $$z\in {\mathbb {R}}^n$$ and $$0 < \varepsilon \ll 1$$ . Our main result is the derivation of com
Publikováno v:
AVITABILE, DANIELE, DESROCHES, MATHIEU, VELTZ, ROMAIN & WECHSELBERGER, MARTIN 2020, ' Local theory for spatio-temporal canards and delayed bifurcations ', SIAM Journal on Mathematical Analysis, vol. 52, no. 6, pp. 5703-5747 . https://doi.org/10.1137/19M1306610
SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), pp.5703-5747. ⟨10.1137/19M1306610⟩
SIAM Journal on Mathematical Analysis, 52(6), 5703-5747. Society for Industrial and Applied Mathematics Publications
SIAM Journal on Mathematical Analysis, 2020, 52 (6), pp.5703-5747. ⟨10.1137/19M1306610⟩
SIAM Journal on Mathematical Analysis
SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), pp.5703-5747. ⟨10.1137/19M1306610⟩
SIAM Journal on Mathematical Analysis, 52(6), 5703-5747. Society for Industrial and Applied Mathematics Publications
SIAM Journal on Mathematical Analysis, 2020, 52 (6), pp.5703-5747. ⟨10.1137/19M1306610⟩
International audience; 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 mode
Publikováno v:
Jelbart, S, Kristiansen, K U & Wechselberger, M 2021, ' Singularly Perturbed Boundary-Equilibrium Bifurcations ', Nonlinearity, vol. 34, no. 11, pp. 7371-7314 . https://doi.org/10.1088/1361-6544/ac23b8
Boundary equilibria bifurcation (BEB) arises in piecewise-smooth systems when an equilibrium collides with a discontinuity set under parameter variation. Singularly perturbed BEB refers to a bifurcation arising in singular perturbation problems which
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::69b62371dcf6e9bc8109bbdc19faa2ae
http://arxiv.org/abs/2103.09613
http://arxiv.org/abs/2103.09613
Autor:
Martin Wechselberger
Publikováno v:
Frontiers in Applied Dynamical Systems: Reviews and Tutorials ISBN: 9783030363987
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::557d647e6384638e05537f3db3351442
https://doi.org/10.1007/978-3-030-36399-4_1
https://doi.org/10.1007/978-3-030-36399-4_1
Autor:
Martin Wechselberger
Publikováno v:
Frontiers in Applied Dynamical Systems: Reviews and Tutorials ISBN: 9783030363987
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a8fd4cbf517217652fcf45bc17f90d11
https://doi.org/10.1007/978-3-030-36399-4_2
https://doi.org/10.1007/978-3-030-36399-4_2
Autor:
Martin Wechselberger
Publikováno v:
Frontiers in Applied Dynamical Systems: Reviews and Tutorials ISBN: 9783030363987
There are important questions in the context of relaxation oscillatory behaviour observed in singularly perturbed systems that we have not addressed so far: where do these oscillations originate from, i.e., what is the underlying mechanism that leads
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::1777d54ee7db6634e0893fa2b078c907
https://doi.org/10.1007/978-3-030-36399-4_6
https://doi.org/10.1007/978-3-030-36399-4_6
Autor:
Martin Wechselberger
Publikováno v:
Frontiers in Applied Dynamical Systems: Reviews and Tutorials ISBN: 9783030363987
This chapter extends the coordinate-independent GSPT beyond Fenichel theory. Loss of normal hyperbolicity is one essential ingredient for a singularly perturbed system to switch between slow and fast dynamics as observed in many relaxation oscillator
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::be0e5cda8aa732ad7a77e50bd2802125
https://doi.org/10.1007/978-3-030-36399-4_4
https://doi.org/10.1007/978-3-030-36399-4_4
Autor:
Martin Wechselberger
Publikováno v:
Frontiers in Applied Dynamical Systems: Reviews and Tutorials ISBN: 9783030363987
As mentioned in the previous chapter, the local dynamics near regular jump points indicate one possibility for solutions of a general singular perturbation problem ( 3.10), respectively, ( 3.15) to switch from slow to fast dynamics (or vice versa) wh
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::b8b2daa1dbdedbb7202ff9cee3c08c32
https://doi.org/10.1007/978-3-030-36399-4_5
https://doi.org/10.1007/978-3-030-36399-4_5