Coupled cell networks


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.

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21 000EUR
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Assistant Professor
Faculdade de Ciências da Universidade do Porto

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