### Multiequilibria analysis for a class of collective decision-making networked systems.

#### A, Fontan and C. Altafini

*IEEE Trans on Control of Network Systems*, to appear, 2017.

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.

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