4 problems

Consider the confined Cucker–Smale system for $N$ agents with initial data $({\bf x}_0,{\bf v}_0)\in\mathbb{R}^{nN}\times\mathbb{R}^{nN}\setminus\mathcal{H}$, where $\mathcal{H}$ i…

Let $N$ agents have initial data $({\bf x}_0,{\bf v}_0)\in\mathbb{T}^{nN}\times\mathbb{R}^{nN}$ and evolve according to the Cucker–Smale system. A cluster is a group of agents shar…

Let $N$ agents have positions ${\bf x}_0\in\mathbb{T}^{nN}$ and velocities ${\bf v}_0\in\mathbb{R}^{nN}$, evolving according to the Cucker–Smale system with a strictly local commun…

Consider the phase diagram of the model parameters governing hallway dynamics, with finite observation time $t_{max}$ and a finite maximal number of agents entering the domain. Let…