Solitary states in the mean-field limit.

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.

[1]  Y. Maistrenko,et al.  Imperfect chimera states for coupled pendula , 2014, Scientific Reports.

[2]  I. Aranson,et al.  The 2020 motile active matter roadmap , 2019, Journal of physics. Condensed matter : an Institute of Physics journal.

[3]  Tomasz Kapitaniak,et al.  Chimera states on the route from coherence to rotating waves. , 2015, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  J. A. Carrillo,et al.  Contractivity of Transport Distances for the Kinetic Kuramoto Equation , 2013, 1301.1883.

[5]  Lorenzo Pareschi,et al.  Structure preserving schemes for the continuum Kuramoto model: Phase transitions , 2018, J. Comput. Phys..

[6]  A. Pikovsky,et al.  Analytical approach to synchronous states of globally coupled noisy rotators , 2019, New Journal of Physics.

[7]  Edgar Knobloch,et al.  Chimerapedia: coherence–incoherence patterns in one, two and three dimensions , 2019, New Journal of Physics.

[8]  Tomasz Kapitaniak,et al.  Solitary states for coupled oscillators with inertia. , 2017, Chaos.

[9]  J. Carrillo,et al.  Traveling bands, clouds, and vortices of chiral active matter. , 2020, Physical review. E.

[10]  A. Lichtenberg,et al.  A First Order Phase Transition Resulting from Finite Inertia in Coupled Oscillator Systems , 1996 .

[11]  Simona Olmi,et al.  Enhancing power grid synchronization and stability through time-delayed feedback control. , 2019, Physical review. E.

[12]  Yuri Maistrenko,et al.  Solitary state at the edge of synchrony in ensembles with attractive and repulsive interactions. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  D. Abrams,et al.  Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators , 2014, 1403.6204.

[14]  Yilin Wu,et al.  Weak synchronization and large-scale collective oscillation in dense bacterial suspensions , 2017, Nature.

[15]  Simona Olmi,et al.  Hysteretic transitions in the Kuramoto model with inertia. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  C. Lancellotti.  On the Vlasov Limit for Systems of Nonlinearly Coupled Oscillators without Noise , 2005 .

[17]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[18]  Tomasz Kapitaniak,et al.  Network-induced multistability through lossy coupling and exotic solitary states , 2020, Nature Communications.

[19]  Andrew J. Archer,et al.  Dynamical density functional theory for interacting Brownian particles: stochastic or deterministic? , 2004, cond-mat/0405603.

[20]  Pierre Degond,et al.  Continuum limit of self-driven particles with orientation interaction , 2007, 0710.0293.

[21]  Y. Maistrenko,et al.  Self-propelled chimeras , 2015, Physical Review E.

[22]  A. Lichtenberg,et al.  Self-synchronization of coupled oscillators with hysteretic responses , 1997 .

[23]  J. Carrillo,et al.  A P ] 9 J an 2 01 3 CONTRACTIVITY OF THE WASSERSTEIN METRIC FOR THE KINETIC KURAMOTO EQUATION , 2013 .

[24]  P. Ashwin,et al.  Weak chimeras in minimal networks of coupled phase oscillators. , 2014, Chaos.

[25]  T. Vicsek,et al.  Collective Motion , 1999, physics/9902023.

[26]  Jos'e A. Carrillo,et al.  A well-posedness theory in measures for some kinetic models of collective motion , 2009, 0907.3901.

[27]  S. Strogatz,et al.  Chimera states for coupled oscillators. , 2004, Physical review letters.

[28]  Eckehard Schöll,et al.  Synchronization patterns and chimera states in complex networks: Interplay of topology and dynamics , 2016 .