|
Network structure and spatiotemporally symmetric
dynamics
Kresimir Josic and Andrew Torok
We examine the relation between the structure of a network and the spatio-temporally
symmetric periodic dynamics it can support. If we are looking for solutions in which
no cell is stationary, then we show that only networks in which all cells interact with
each other, or which contain a single group of interacting cells which drive the remainder
of the network can exhibit such dynamics robustly. These characteristics
of network architecture are not captured by the typical statistical quantities used to
describe network structure.We illustrate the existence of spatio-temporally periodic
solutions through a direct construction using ideas from coupled cell theory and the
theory of weakly coupled oscillators, and show that these solutions can be stable
in a very large region of parameter space. While we consider only a special type of
network behavior, these ideas extend to more general architectures and dynamics.
PDF
|
|
|
______________________________________________________________________________________________
Current Address: Department of Mathematics, PGH Building, University of Houston, Houston, Texas 77204-3008
Phone: (713) 743-3500 - Fax: (713) 743-3505
|
|
