Leader-follower consensus and synchronization in numerosity-constrained networks with dynamic leadership

Leader-follower consensus on activity-driven networks

Social groups such as schools of fish or flocks of birds display collective dynamics that can be modulated by group leaders, which facilitate decision-making toward a consensus state beneficial to the entire group. For instance, leaders could alert the group about attacking predators or the presence of food sources. Motivated by biological insight on social groups, we examine a stochastic leader-follower consensus problem where information sharing among agents is affected by perceptual constraints and each individual has a different tendency to form social connections. Leveraging tools from stochastic stability and eigenvalue perturbation theories, we study the consensus protocol in a mean-square sense, offering necessary-and-sufficient conditions for asymptotic stability and closed-form estimates of the convergence rate. Surprisingly, the prediction of our minimalistic model share similarities with observed traits of animal and human groups. Our analysis anticipates the counterintuitive result that heterogeneity can be beneficial to group decision-making by improving the convergence rate of the consensus protocol. This observation finds support in theoretical and empirical studies on social insects such as spider or honeybee colonies, as well as human teams, where inter-individual variability enhances the group performance.

Introduction: Collective dynamics of mechanical oscillators and beyond

This focus issue presents a collection of research papers from a broad spectrum of topics related to the modeling, analysis, and control of mechanical oscillators and beyond. Examples covered in this focus issue range from bridges and mechanical pendula to self-organizing networks of dynamic agents, with application to robotics and animal grouping. This focus issue brings together applied mathematicians, physicists, and engineers to address open questions on various theoretical and experimental aspects of collective dynamics phenomena and their control.