The hyperbolic model for edge and texture detection in the primary visual cortex
P Chossat - The Journal of Mathematical Neuroscience, 2020 - Springer
The modeling of neural fields in the visual cortex involves geometrical structures which
describe in mathematical formalism the functional architecture of this cortical area. The case …
describe in mathematical formalism the functional architecture of this cortical area. The case …
Symmetry methods in mathematical biology
M Golubitsky, I Stewart - São Paulo Journal of Mathematical Sciences, 2015 - Springer
Many biological systems have aspects of symmetry. Symmetry is formalized using group
theory. This theory applies not just to the geometry of symmetric systems, but to their …
theory. This theory applies not just to the geometry of symmetric systems, but to their …
Asymptotic Stability of Pseudo-simple Heteroclinic Cycles in
O Podvigina, P Chossat - Journal of Nonlinear Science, 2017 - Springer
Robust heteroclinic cycles in equivariant dynamical systems in\mathbb R^ 4 R 4 have been
a subject of intense scientific investigation because, unlike heteroclinic cycles in\mathbb R …
a subject of intense scientific investigation because, unlike heteroclinic cycles in\mathbb R …
Localized states in an unbounded neural field equation with smooth firing rate function: a multi-parameter analysis
The existence of spatially localized solutions in neural networks is an important topic in
neuroscience as these solutions are considered to characterize working (short-term) …
neuroscience as these solutions are considered to characterize working (short-term) …
Simple heteroclinic cycles in R^ 4
O Podvigina, P Chossat - arXiv preprint arXiv:1310.0298, 2013 - arxiv.org
In generic dynamical systems heteroclinic cycles are invariant sets of codimension at least
one, but they can be structurally stable in systems which are equivariant under the action of …
one, but they can be structurally stable in systems which are equivariant under the action of …
Classification and stability of simple homoclinic cycles in
O Podvigina - Nonlinearity, 2013 - iopscience.iop.org
Heteroclinic cycles, unions of equilibria and connection trajectories, can be structurally
stable in a Γ-equivariant system due to the existence of invariant subspaces. A structurally …
stable in a Γ-equivariant system due to the existence of invariant subspaces. A structurally …
Localized radial bumps of a neural field equation on the Euclidean plane and the Poincaré disc
We analyse radially symmetric localized bump solutions of an integro-differential neural field
equation posed in Euclidean and hyperbolic geometry. The connectivity function and the …
equation posed in Euclidean and hyperbolic geometry. The connectivity function and the …
A spatialized model of textures perception using structure tensor formalism
G Faye, P Chossat - Networks and Heterogeneous Media, 2013 - hal.science
The primary visual cortex (V1) can be partitioned into fundamental domains or
hypercolumns consisting of one set of orientation columns arranged around a singularity …
hypercolumns consisting of one set of orientation columns arranged around a singularity …
Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane
P Chossat, G Faye - Journal of Dynamics and Differential Equations, 2015 - Springer
In this paper we present an overview of pattern formation analysis for an analogue of the
Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we …
Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we …
[PDF][PDF] Very simple heteroclinic cycles in R4
O Podvigina, P Chossat - arXiv preprint arXiv:1310.0298, 2013 - Citeseer
In generic dynamical systems heteroclinic cycles are invariant sets of codimension at least
one, but they can be structurally stable in systems which are equivariant under the action of …
one, but they can be structurally stable in systems which are equivariant under the action of …