Title: Multiequilibria analysis for a class of collective decision-making networked systems,
Abstract: The models of collective decision-making considered in this paper are
nonlinear interconnected cooperative systems with saturating interactions.
These systems encode the possible outcomes of a decision process into different
steady states of the dynamics. In particular, they are characterized by two
main attractors in the positive and negative orthant, representing two choices
of agreement among the agents, associated to the Perron-Frobenius eigenvector
of the system. In this paper we give conditions for the appearance of other
equilibria of mixed sign. The conditions are inspired by Perron-Frobenius
theory and are related to the algebraic connectivity of the network. We also
show how all these equilibria must be contained in a solid disk of radius given
by the norm of the equilibrium point which is located in the positive orthant.