Related papers: Singular Cucker-Smale Dynamics
We present a sufficient condition of the complete position flocking theorem for the Cucker-Smale type model on the unit sphere with an inter-particle bonding force. For this second order dynamical system derived in [Choi, S.-H., Kwon, D.…
We study the existence and uniqueness of the time evolution of a system of infinitely many individuals, moving in a tunnel and subjected to a Cucker-Smale type alignment dynamics with compactly supported communication kernels and to…
We analyse the asymptotic behavior for kinetic models describing the collective behavior of animal populations. We focus on models for self-propelled individuals, whose velocity relaxes toward the mean orientation of the neighbors. The…
We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the…
We introduce a multi-dimensional variant of the kinetic Cucker-Smale model with singular and matrix-valued communication weight, which reduces to the singular kinetic Cucker-Smale equation in the one-dimensional case. We propose an…
In this paper, we study the singular Cucker-Smale (C-S) model on the real line. For long range case, i.e. $\beta<1$, we prove the uniqueness of the solution in the sense of Definition 2.1 and the unconditional flocking emergence. Moreover,…
For the discrete Cucker-Smale's flocking model with a singular communication weight $\psi(s) = s^{-\alpha}$, with $0<\alpha<1/2$ , we prove that the velocity component of certain type of weak solutions is absolutly continuous. This result…
We study the large-time behavior of continuum alignment dynamics based on Cucker-Smale (CS)-type interactions which involve short-range kernels, that is, communication kernels with support much smaller than the diameter of the crowd. We…
We derive an explicit form for the Cucker-Smale (CS) model on the special orthogonal group $\mathrm{SO}(3)$ by identifying closed form expressions for geometric quantities such as covariant derivative and parallel transport in exponential…
We prove existence of global $C^1$ piecewise weak solutions for the discrete Cucker-Smale's flocking model with the communication weight $\psi(s)=s^{-\alpha}, 0<\alpha<1.$ We also discuss the possibility of finite in time alignment of the…
We present collective dynamics of the Cucker-Smale (C-S) ensemble under random communications. As an effective modeling of the C-S ensemble, we introduce a stochastic kinetic C-S equation with a multiplicative white noise. For the proposed…
We study dynamic interplay between time-delay and velocity alignment in the ensemble of Cucker-Smale (C-S) particles(or agents) on time-varying networks which are modeled by digraphs containing spanning trees. Time-delayed dynamical systems…
We study the emergent dynamics of the relativistic kinetic Cucker-Smale (RKCS) model without assuming compactness in spatial and velocity support. In this setting, the lower bound of the kernel function in the nonlocal velocity alignment…
In this note, we consider generalizations of the Cucker-Smale dynamical system and we derive rigorously in Wasserstein's type topologies the mean-field limit (and propagation of chaos) to the Vlasov-type equation introduced in [12].Unlike…
We study a Cucker-Smale-type flocking model with distributed time delay where individuals interact with each other through normalized communication weights. Based on a Lyapunov functional approach, we provide sufficient conditions for the…
In this paper, we study sufficient conditions for the emergence of asymptotic consensus and flocking in a certain class of non-linear generalised Cucker-Smale systems subject to multiplicative communication failures. Our approach is based…
We establish the global existence of weak solutions to a class of kinetic flocking equations. The models under consideration include the kinetic Cucker-Smale equation with possibly non-symmetric flocking potential, the Cucker-Smale equation…
In this work, we perform modulation analysis of monokinetic limits from the kinetic Cucker- Smale model to the pressureless Euler alignment system. Two regimes are considered -- a strong Fokker- Planck force with vanishing noise and Knudsen…
A mathematical theory on flocking serves the foundation for several ubiquitous multi-agent phenomena in biology, ecology, sensor networks, economy, as well as social behavior like language emergence and evolution. Directly inspired by the…
A coupled kinetic-fluid model is investigated, which describes the dynamic behavior of an ensemble of Cucker-Smale flocking particles interacting with a viscous fluid in a three-dimensional bounded domain. This system consists of a kinetic…