Synchronism in population networks with non linear coupling

A quite general spatially explicit metapopulation model featuring density-dependent dispersal is proposed. A study of the stability of synchronized attractors is done based on an explicit calculation of the transverse Lyapunov number of these attractors. An analytic expression for the transverse Lyapunov number depending on the Lyapunov number of the synchronous trajectory, the eigenvalues of the network configuration matrix and the function modelling the density-dependent dispersal (the number of migrants as a function of the local density) is presented. Numerical simulations are also performed upon selecting biologically relevant features, such as local dynamics, network topology and density-dependent dispersal mechanism.