Hopf Bifurcation in Coupled Cell Networks with Interior Symmetries

DOI10.1137/070684604zbMath1169.34321OpenAlexW2036153627MaRDI QIDQ3624444

Fernando Antoneli, Rui C. Paiva, Ana Paula S. Dias

Publication date: 30 April 2009

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/79c63f78b1814bcb487e57b81df004bc9b44d589

zbMATH Keywords

bifurcation theorycoupled cell networksinterior symmetries

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Neural networks for/in biological studies, artificial life and related topics (92B20) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15)

Related Items (14)

Center Manifolds of Coupled Cell Networks ⋮ Chaotic behavior in diffusively coupled systems ⋮ Topology and bifurcations in Hamiltonian coupled cell systems ⋮ Projection blocks in homogeneous coupled cell networks ⋮ Dynamics of coupled cell networks: synchrony, heteroclinic cycles and inflation ⋮ Center Manifolds of Coupled Cell Networks ⋮ Circulant type formulas for the eigenvalues of linear network maps ⋮ Bifurcations in dynamical systems with interior symmetry ⋮ Periodic solutions in an array of coupled FitzHugh-Nagumo cells ⋮ Quasi-periodic states in coupled rings of cells ⋮ Graph fibrations and symmetries of network dynamics ⋮ Hidden Symmetries, Coupled Networks and Equivariant Degrees ⋮ EXOTIC DYNAMICS IN NETWORKS OF COUPLED RINGS OF CELLS ⋮ Coupled cell networks: Semigroups, Lie algebras and normal forms

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