Network dynamics with higher-order interactions: coupled cell hypernetworks for identical cells and synchrony

NONLINEARITY

2023 | journal-article

Synchrony patterns in gene regulatory networks

PHYSICA D-NONLINEAR PHENOMENA

2022 | review

Towards a classification of networks with asymmetric inputs

Nonlinearity

2021 | journal-article

Synchrony and Antisynchrony in Weighted Networks

SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

2021 | journal-article

Characterization of fundamental networks

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

2020 | journal-article

Feedforward Networks: Adaptation, Feedback, and Synchrony

Journal of Nonlinear Science

2019 | journal-article

Gradient and Hamiltonian coupled systems on undirected networks

Mathematical Biosciences and Engineering

2019 | journal-article

The steady-state lifting bifurcation problem associated with the valency on networks

Physica D: Nonlinear Phenomena

2019 | journal-article

An overview of synchrony in coupled cell networks

Springer Proceedings in Mathematics and Statistics

2018 | conference-paper

Direct lifts of coupled cell networks

Nonlinearity

2018 | journal-article

Synchronization and equitable partitions in weighted networks

Chaos

2018 | journal-article

Heteroclinic network dynamics on joining coupled cell networks

Dynamical Systems

2017 | journal-article

Patterns of synchrony for feed-forward and auto-regulation feed-forward neural networks

Chaos

2017 | journal-article

Synchrony and elementary operations on coupled cell networks

SIAM Journal on Applied Dynamical Systems

2016 | journal-article

Regular synchrony lattices for product coupled cell networks

Chaos

2015 | journal-article

The Lattice of Synchrony Subspaces of a Coupled Cell Network: Characterization and Computation Algorithm

Journal of Nonlinear Science

2014 | journal-article

Spectrum of the elimination of loops and multiple arrows in coupled cell networks

Nonlinearity

2012 | journal-article

Coupled cell networks: Hopf bifurcation and interior symmetry

Discrete and Continuous Dynamical Systems- Series A

2011 | journal-article

Dynamics of coupled cell networks: Synchrony, heteroclinic cycles and inflation

Journal of Nonlinear Science

2011 | journal-article

Enumerating periodic patterns of synchrony via finite bidirectional networks

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

2010 | journal-article

Quasi-periodic states in coupled rings of cells

Communications in Nonlinear Science and Numerical Simulation

2010 | journal-article

Bifurcations from regular quotient networks: A first insight

Physica D: Nonlinear Phenomena

2009 | journal-article

Generating functions for hopf bifurcation with Sn-symmetry

Discrete and Continuous Dynamical Systems

2009 | journal-article

Hopf bifurcation with SN-symmetry

Nonlinearity

2009 | journal-article

Invariant theory and reversible-equivariant vector fields

Journal of Pure and Applied Algebra

2009 | journal-article

Spatially periodic patterns of synchrony in lattice networks

SIAM Journal on Applied Dynamical Systems

2009 | journal-article

Hopf bifurcation in coupled cell networks with interior symmetries

SIAM Journal on Applied Dynamical Systems

2008 | journal-article

Invariants, equivariants and characters in symmetric bifurcation theory

Proceedings of the Royal Society of Edinburgh Section A: Mathematics

2008 | journal-article

Homogeneous coupled cell networks with S3-Symmetric quotient

Discrete and Continuous Dynamical Systems- Series A

2007 | journal-article

Minimal coupled cell networks

Nonlinearity

2007 | journal-article

A note on Hopf bifurcation with dihedral group symmetry

Glasgow Mathematical Journal

2006 | journal-article

Flow invariant subspaces for lattice dynamical systems

BIFURCATION THEORY AND SPATIO-TEMPORAL PATTERN FORMATION

2006 | conference-paper

Hopf bifurcation on hemispheres

Nonlinearity

2006 | journal-article

Local bifurcation in symmetric coupled cell networks: Linear theory

Physica D: Nonlinear Phenomena

2006 | journal-article

Secondary bifurcations in systems with all-to-all coupling. Part II

Dynamical Systems

2006 | journal-article

Linear equivalence and ODE-equivalence for coupled cell networks

Nonlinearity

2005 | journal-article

Patterns of synchrony in lattice dynamical systems

Nonlinearity

2005 | journal-article

Symmetry groupoids and admissible vector fields for coupled cell networks

Journal of the London Mathematical Society

2004 | journal-article

Secondary bifurcations in systems with all-to-all coupling

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

2003 | journal-article

Heteroclinic cycles and wreath product symmetries

Dynamical Systems

2000 | journal-article

Hilbert series for equivariant mappings restricted to invariant hyperplanes

Journal of Pure and Applied Algebra

2000 | journal-article

Invariant theory for wreath product groups

Journal of Pure and Applied Algebra

2000 | journal-article

Toric geometry and equivariant bifurcations

Physica D: Nonlinear Phenomena

2000 | journal-article

Hopf bifurcation on a simple cubic lattice

Dynamical Systems

1999 | journal-article

Hopf bifurcation on a simple cubic lattice

Dynamics and Stability of Systems

1999 | journal-article

Symmetry-breaking bifurcations of wreath product systems

Journal of Nonlinear Science

1999 | journal-article

Hopf bifurcation for wreath products

Nonlinearity

1998 | journal-article

Instant chaos is chaos in slow motion

Journal of Mathematical Analysis and Applications

1996 | journal-article