Solitary states in the mean-field limit

Abstract

We study active matter systems where the orientational dynamics of underlying self-propelled particles obey second order equations. By primarily concentrating on a spatially homogeneous setup for particle distribution, our analysis combines theories of active matter and oscillatory networks. For such systems, we analyze the appearance of solitary states via a homoclinic bifurcation as a mechanism of the frequency clustering. By introducing noise, we establish a stochastic version of solitary states and derive the mean-field limit described by a partial differential equation for a one-particle probability density function, which one might call the continuum Kuramoto model with inertia and noise. By studying this limit, we establish second order phase transitions between polar order and disorder. The combination of both analytical and numerical approaches in our study demonstrates an excellent qualitative agreement between mean-field and finite size models.

References in corpus (20)

• Novel type of phase transition in a system of self-driven particles
• Collective motion
• Chimera States for Coupled Oscillators
• Chimera states: Coexistence of coherence and incoherence in networks of coupled oscillators
• Coexistence of Coherence and Incoherence in Nonlocally Coupled Phase Oscillators
• The 2019 Motile Active Matter Roadmap
• A well-posedness theory in measures for some kinetic models of collective motion
• Continuum limit of self-driven particles with orientation interaction
• Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic?
• Weak chimeras in minimal networks of coupled phase oscillators
• Hysteretic transitions in the Kuramoto model with inertia
• Solitary state at the edge of synchrony in ensembles with attractive and repulsive interaction
• Solitary states for coupled oscillators
• Enhancing power grid synchronization and stability through time delayed feedback control
• Solitary states in adaptive nonlocal oscillator networks
• Contractivity of the Wasserstein metric for the kinetic Kuramoto equation
• Traveling Bands, Clouds, and Vortices of Chiral Active Matter
• Self-propelled chimeras
• Structure preserving schemes for the continuum Kuramoto model: phase transitions
• A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles

Cited by in corpus (6)

• Unbalanced clustering and solitary states in coupled excitable systems
• Solitary states in multiplex neural networks: onset and vulnerability
• Generalized splay states in phase oscillator networks
• Mixed-Mode Chimera states in Pendula Networks
• Solitary routes to chimera states
• Chimera states for directed networks