Large scale dynamics of the Persistent Turning Walker model of fish behavior

Abstract

This paper considers a new model of individual displacement, based on fish motion, the so-called Persistent Turning Walker (PTW) model, which involves an Ornstein-Uhlenbeck process on the curvature of the particle trajectory. The goal is to show that its large time and space scale dynamics is of diffusive type, and to provide an analytic expression of the diffusion coefficient. Two methods are investigated. In the first one, we compute the large time asymptotics of the variance of the individual stochastic trajectories. The second method is based on a diffusion approximation of the kinetic formulation of these stochastic trajectories. The kinetic model is a Fokker-Planck type equation posed in an extended phase-space involving the curvature among the kinetic variables. We show that both methods lead to the same value of the diffusion constant. We present some numerical simulations to illustrate the theoretical results.

References in corpus (5)

• Novel type of phase transition in a system of self-driven particles
• Traffic and Related Self-Driven Many-Particle Systems
• Onset of collective and cohesive motion
• Collective Behavior of Self Propelling Particles with Kinematic Constraints; The relation between the discrete and the continuous description
• Hydrodynamic Model for the System of Self Propelling Particles with Conservative Kinematic Constraints; Two dimensional stationary solutions

Cited by in corpus (16)

• A new model for self-organized dynamics and its flocking behavior
• Hydrodynamic equations for self-propelled particles: microscopic derivation and stability analysis
• Swarming, Schooling, Milling: Phase diagram of a data-driven fish school model
• Macroscopic limits and phase transition in a system of self-propelled particles
• A continuum model for alignment of self-propelled particles with anisotropy and density-dependent parameters
• Active motion assisted by correlated stochastic torques
• Diffusion in a continuum model of self-propelled particles with alignment interaction
• A macroscopic model for a system of swarming agents using curvature control
• Congestion in a macroscopic model of self-driven particles modeling gregariousness
• Emergent behaviors of the Cucker-Smale ensemble under attractive-repulsive couplings and Rayleigh frictions
• Emergent behaviors of Cucker-Smale flocks on the hyperboloid
• Pattern formation of a nonlocal, anisotropic interaction model
• Diffusion of Active Particles With Stochastic Torques Modeled as $\alpha$-Stable Noise
• Gaussian Memory in Kinematic Matrix Theory for Self-Propellers
• Model of metameric locomotion in active directional filaments
• Stability analysis of line patterns of an anisotropic interaction model