# Emergent Behavior in Flocks

@article{Cucker2007EmergentBI, title={Emergent Behavior in Flocks}, author={Felipe Cucker and Stephen Smale}, journal={IEEE Transactions on Automatic Control}, year={2007}, volume={52}, pages={852-862} }

We provide a model (for both continuous and discrete time) describing the evolution of a flock. Our model is parameterized by a constant beta capturing the rate of decay-which in our model is polynomial-of the influence between birds in the flock as they separate in space. Our main result shows that when beta<1/2 convergence of the flock to a common velocity is guaranteed, while for betages1/2 convergence is guaranteed under some condition on the initial positions and velocities of the birds…

## 1,403 Citations

### On flocks influenced by closest neighbors

- Mathematics
- 2016

We prove, both for continuous time and discrete time, results establishing convergence to flocking in a model in which each agent is influenced by only a few closest neighbors. We show unconditional…

### A Generalized Model of Flocking with Steering

- Computer ScienceSIAM J. Appl. Dyn. Syst.
- 2022

This work introduces and analyzes a model for the dynamics of flocking and steering of a finite number of agents and provides rigorous sufficient conditions under which the agents flock and steer together.

### Emergence of flocks with local interactions

- MathematicsProceedings of the 10th World Congress on Intelligent Control and Automation
- 2012

In a recent paper, Cucker and Smale proposed a multi-agent model to study the flocking behavior, where they assume that all agents can interact with all other agents. Though this model attracted much…

### The geometry of flocking

- Computer ScienceSCG
- 2010

An intriguing geometric object, the "flight net", is introduced, and the idea of a "virtual agent" is developed, which gives insight into early flocking behavior in the Vicsek-Cucker-Smale model.

### Emergent behaviors in group ring flocks

- Mathematics, Economics
- 2020

We present a first-order aggregation model on a group ring, and study its asymptotic dynamics. In a positive coupling strength regime, we show that the flow generated by the proposed model tends to…

### Impacts of time delay on flocking dynamics of a two-agent flock model

- EngineeringCommun. Nonlinear Sci. Numer. Simul.
- 2019

### Uniform-in-time bound for kinetic flocking models

- Mathematics, Computer ScienceAppl. Math. Lett.
- 2020

### Avoiding Collisions in Flocks

- MathematicsIEEE Transactions on Automatic Control
- 2010

This note extends the model for flocking systems of interacting particles by adding to it a repelling force between particles, and shows that, for this modified model, convergence to flocking is established along the same lines while avoidance of collisions is ensured.

### Flocking and non-flocking behavior in a stochastic Cucker-Smale system

- Mathematics
- 2015

We first present a new stochastic version of the Cucker-Smale model of the emergent behavior in flocks in which the mutual communication between individuals is affected by random factor. Then, the…

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