Stabilization mechanism of amplitude death in a high-dimensional map network with a connection delay*

This paper investigates a stabilization mechanism of amplitude death in a high-dimensional map network with a connection delay. Three types of nonlinear maps are employed to reveal the mechanism. The root locus of a simplified characteristic equation allows us to understand the mechanism: an unstable uniform equilibrium state is stabilized through repetition of a bifurcation, where the number of the repetitions is equal to the number of maps in the network.