Fig. 5: Heterogeneity-induced stability in consensus dynamics with time delay.
From: Optimal flock formation induced by agent heterogeneity
a Lyapunov exponent \({\Lambda }_{\max }\) as a function of the time delay τ for an optimal flock of heterogeneous (blue) and homogeneous (orange) agents for N = 4. Consensus is stable (unstable) for all initial conditions x(0) if \({\Lambda }_{\max } < 0\) (\({\Lambda }_{\max } > 0\)). A flock is said to be optimal if the choice of parameters ki minimizes \({\Lambda }_{\max }\). b Dynamical evolution of the agents' positions qi(t) for an optimal flock of heterogeneous (top) and homogeneous (bottom) agents. The time delay is set as τ = 0.6. See SI, Section S4, for details on the optimization problem.
