Synchronization of weakly coupled oscillators is ubiquitous in biological and chemical
complex systems. Recently, research on collective dynamics of many-body systems has …

This survey summarizes and illustrates the main qualitative properties of hydrodynamics
models for collective behavior. These models include a velocity consensus term together …

The description of emerging collective phenomena and self-organization in systems
composed of large numbers of individuals has gained increasing interest from various …

SI can be seen also as part of the broader field of computational intelligence (CI)(Keller et al.
2016), which comprises computational methods for problems not solvable by the first …

We review the state-of-the-art in the modelling of the aggregation and collective behavior of
interacting agents of similar size and body type, typically called swarming. Starting with …

These notes are devoted to a summary on the mean-field limit of large ensembles of
interacting particles with applications in swarming models. We first make a summary of the …

We consider general stochastic systems of interacting particles with noise which are relevant
as models for the collective behavior of animals, and rigorously prove that in the mean-field …

In this chapter, we present the Cucker–Smale-type flocking models and discuss their
mathematical structures and flocking theorems in terms of coupling strength, interaction …

We introduce the concept of mean-field optimal control which is the rigorous limit process
connecting finite dimensional optimal control problems with ODE constraints modeling multi …

Abstract We consider the Cucker–Smale flocking model with a singular communication
weight ψ (s)= s− α with α> 0. We provide a critical value of the exponent α in the …