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.

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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