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Singularities and groups in bifurcation theory

This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob- lems and we hope to convert the reader to this…
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Stable mappings and their singularities

I: Preliminaries on Manifolds.- 1. Manifolds.- 2. Differentiable Mappings and Submanifolds.- 3. Tangent Spaces.- 4. Partitions of Unity.- 5. Vector Bundles.- 6. Integration of Vector Fields.- II:…
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Patterns of Synchrony in Coupled Cell Networks with Multiple Arrows

TLDR
A framework for coupled cell systems that permits a classification of robust synchrony in terms of network architecture and the existence of other robust dynamical patterns using a concept of quotient network is presented.
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Singularities and Groups in Bifurcation Theory: Volume I

Symmetry Groupoids and Patterns of Synchrony in Coupled Cell Networks

A coupled cell system is a network of dynamical systems, or "cells," coupled together. Such systems can be represented schematically by a directed graph whose nodes correspond to cells and whose…
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The Symmetry Perspective: From Equilibrium to Chaos in Phase Space and Physical Space

1. Steady-State Bifurcation.- 1.1. Two Examples.- 1.2. Symmetries of Differential Equations.- 1.3. Liapunov-Schmidt Reduction.- 1.4. The Equivariant Branching Lemma.- 1.5. Application to Speciation.-…

Nonlinear dynamics of networks: the groupoid formalism

A formal theory of symmetries of networks of coupled dynamical systems, stated in terms of the group of permutations of the nodes that preserve the network topology, has existed for some time.…
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The Symmetry Perspective

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Hopf Bifurcation in the presence of symmetry

Using group theoretic techniques, we obtain a generalization of the Hopf Bifurcation Theorem to differential equations with symmetry, analogous to a static bifurcation theorem of Cicogna. We discuss…
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Pattern selection with O(3) symmetry

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