| 概要 | A coupled cell system is a network of dynamical systems, or 'cells',
each of which is given by ODEs. The network architecture is
a directed graph and it represents interactions between the
dynamical systems on cells. The main motivation of the study of
coupled cell system, formulated by M. Golubitsky, I. Stewart et
al., is to understand dynamics of the whole system from its network
architecture. As the number of cells in the network grows the coupled
cell system would be more and more complicated to analyse. To meet
such difficulty, we develop an idea of getting at least partial
information of the system from its subnetwork architecture. We
show that for a certain type of network and a generic coupled
cell system associated with that network, there exists a local
invariant manifold given in a neighborhood of equilibrium, on which
the coupled cell system behaves identically the same as a coupled
cell system associated with a subnetwork of the original network. |