Existence and uniqueness of solutions for a continuous-time opinion dynamics model with state-dependent connectivity
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We prove that the continuous-time discrete-agent system studied in [1] admits a unique solution for almost all initial conditions. We consider the following continuous-time model: each of n agents, labeled 1, . . . , n, maintains a real number xi(t), which is a continuous function of time, and evolves according to xi(t) = xi(0) + ∫ t
[1] John M. Lee. Introduction to Smooth Manifolds , 2002 .
[2] John N. Tsitsiklis,et al. Continuous-Time Average-Preserving Opinion Dynamics with Opinion-Dependent Communications , 2009, SIAM J. Control. Optim..