Coupled cell networks (Redes de Células acopladas)

Coordinator: 

Ana Paula Dias

Duration: 

3 years+3 months 03/05-05

Research area: 

Mathematics/Dynamical Systems

We call a coupled cell network (CCN) a set of ordinary differential equations (ODEs) (the cells) that are coupled together.We study bifurcations (steady-state and Hopf) and dynamics of CCNs according to: the symmetry, the topology and the symmetry groupoid of the couplings network, and the cell´s internal symmetries. We aim to: - clarify the relation between the bifurcations of symmetric CCNs and those of symmetric ODEs systems; study steady-state bifurcations for CCNs with spherical internal symmetry; study Hopf bifurcation for CCNs with all-to-all coupling and with the cells coupled in a ring; - study Hopf bifurcation with groupoid symmetries; characterize normal forms for ODE-equivalence classes of CCNs; study bifurcations of CCNs of neurons; look for balanced k-colorings patterns of lattices (in 2 and 3 dimensions) CCNs and characterize the dynamics on the corresponding (synchronous) flow-invariant subspaces.

Members: 

Stella Abreu, Manuela Aguiar, Ana Paula Dias, Rui Paiva, Eliana Pinho, Carla Pinto and Ana Margarida Rodrigues.

Other members: 

Hugo Fernandes.

Financial support: 

FCT/FEDER/OE Reference: POCI/MAT/60154/2004 - Matemática