A new model for self-organized dynamics and its flocking behavior

Abstract

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 influence between agents is scaled in term of their relative distance. Consequently, our model does not involve any explicit dependence on the number of agents; only their geometry in phase space is taken into account. The use of relative distances destroys the symmetry property of the original C-S model, which was the key for the various recent studies of C-S flocking behavior. To this end, we introduce here a new framework to analyze the phenomenon of flocking for a rather general class of dynamical systems, which covers systems with non-symmetric influence matrices. In particular, we analyze the flocking behavior of the proposed model as well as other strongly asymmetric models with "leaders". The methodology presented in this paper, based on the notion of active sets, carries over from the particle to kinetic and hydrodynamic descriptions. In particular, we discuss the hydrodynamic formulation of our proposed model, and prove its unconditional flocking for slowly decaying influence functions.

References in corpus (2)

• Novel type of phase transition in a system of self-driven particles
• Interaction Ruling Animal Collective Behaviour Depends on Topological rather than Metric Distance: Evidence from a Field Study

Cited by in corpus (75)

• Quantitative estimate of propagation of chaos for stochastic systems with $W^{-1,\infty }$ kernels
• Critical thresholds in flocking hydrodynamics\\with nonlocal alignment
• Invisible control of self-organizing agents leaving unknown environments
• Flocking estimates for the Cucker-Smale model with time lag and hierarchical leadership
• Euler-type equations and commutators in singular and hyperbolic limits of kinetic Cucker-Smale models
• Flocking dynamics and mean-field limit in the Cucker-Smale-type model with topological interactions
• Global regularity for the fractional Euler alignment system
• Eulerian dynamics with a commutator forcing III. Fractional diffusion of order $0<\alpha <1$
• Phase transition and diffusion among socially interacting self-propelled agents
• Biological Modelling with Nonlocal Advection Diffusion Equations
• Collective motion patterns of swarms with delay coupling: theory and experiment
• Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions
• Evolution of wealth in a nonconservative economy driven by local Nash equilibria
• Kinetic models of collective decision-making in the presence of equality bias
• Flocking and non-flocking behavior in a stochastic Cucker-Smale system
• Singular Cucker-Smale Dynamics
• Global classical solutions of the Vlasov-Fokker-Planck equation with local alignment forces
• Mathematical models and methods for crowd dynamics control
• Consensus Formation in First-Order Graphon Models with Time-Varying Topologies
• A Boltzmann model for rod alignment and schooling fish
• Direct proof of unconditional asymptotic consensus in the Hegselmann-Krause model with transmission-type delay
• A kinetic description for the herding behavior in financial market
• Emergent behaviors of the Cucker-Smale ensemble under attractive-repulsive couplings and Rayleigh frictions
• Flocking with short-range interactions
• First-order aggregation models with alignment
• A multi-layer model for self-propelled disks interacting through alignment and volume exclusion
• Phase transitions and macroscopic limits in a BGK model of body-attitude coordination
• Interacting particles with Lévy strategies: limits of transport equations for swarm robotic systems
• Kinetic models for topological nearest-neighbor interactions
• Emergent behaviors of Cucker-Smale flocks on the hyperboloid
• Controlled pattern formation of stochastic Cucker-Smale systems with network structures
• Stable Swarming Using Adaptive Long-range Interactions
• A discontinuous Galerkin method on kinetic flocking models
• Density-induced Consensus Protocol
• BV solutions for a hydrodynamic model of flocking--type with all-to-all interaction kernel
• Random Feature Models for Learning Interacting Dynamical Systems
• Convergence to consensus for a Hegselmann-Krause-type model with distributed time delay
• Weak and Strong Solutions to the Forced Fractional Euler Alignment System
• The Dynamics of Interacting Swarms
• Model predictive control with random batch methods for a guiding problem
• Bulk topological states in a new collective dynamics model
• Kinetic description and macroscopic limit of swarming dynamics with continuous leader-follower transitions
• Asymptotic flocking for the Cucker-Smale model with time variable time delays
• On the control of the Hegselmann-Krause model with leadership and time delay
• Microscopic modeling and analysis of collective decision making: equality bias leads suboptimal solutions
• Body-attitude coordination in arbitrary dimension
• From Kinetic Flocking Model of Cucker-Smale Type to Self-Organized Hydrodynamic model
• On the mean-field limit for the Vlasov-Poisson-Fokker-Planck system
• Patterned Dynamics of Delay-Coupled Swarms with Random Communication Graphs
• Complete classification of the asymptotical behavior for singular C-S Model on the real line
• Hydrodynamic limits for kinetic flocking models of Cucker-Smale type
• The Emergence of Lines of Hierarchy in Collective Motion of Biological Systems
• Uniform-in-time propagation of chaos for the Cucker--Smale model
• Emergent behaviors of continuous and discrete thermomechanical Cucker-Smale models on general digraphs
• Some aspects of the inertial spin model for flocks and related kinetic equations
• Macroscopic limit of a Fokker-Planck model of swarming rigid bodies
• Models of Animal Behavior as Active Particle Systems with Nonreciprocal Interactions
• Dynamics And Kinetic Limit For A System Of Noiseless D-Dimensional Vicsek-Type Particles
• A simple proof of asymptotic consensus in the Hegselmann-Krause and Cucker-Smale models with renormalization and delay
• On the stochastic flocking of the Cucker-Smale flock with randomly switching topologies
• Emergence of stochastic flocking for the discrete Cucker-Smale model with randomly switching topologies
• A particle model for the herding phenomena induced by dynamic market signals
• Wave turbulence and collective behavior models for wave equations with short- and long-range interactions
• Invariance of velocity angles and flocking in the Inertial Spin model
• Emergent behaviors of the discrete-time Kuramoto model for generic initial configuration
• Existence of martingale solutions for stochastic flocking models with local alignment
• Existence and hydrodynamic limit for a Paveri-Fontana type kinetic traffic model
• Collective stochastic dynamics of the Cucker-Smale ensemble under uncertain communications
• A non-linear kinetic model of self-propelled particles with multiple equilibria
• Flocking of the Cucker-Smale and Motsch-Tadmor models on general weighted digraphs via a probabilistic method
• A Potential Space Estimate for Solutions of Systems of Nonlocal Equations in Peridynamics
• Asymptotic Fixed-Speed Reduced Dynamics for Kinetic Equations in Swarming
• Interplay of time-delay and velocity alignment in the Cucker-Smale model on a general digraph
• Hydrodynamic limit of a coupled Cucker-Smale system with strong and weak internal variable relaxation
• A kinetic approach to active rod dynamics in confined domains