Volcano Transition in a Solvable Model of Frustrated Oscillators.

In 1992, a puzzling transition was discovered in simulations of randomly coupled limit-cycle oscillators. This so-called volcano transition has resisted analysis ever since. It was originally conjectured to mark the emergence of an oscillator glass, but here we show it need not. We introduce and solve a simpler model with a qualitatively identical volcano transition and find that its supercritical state is not glassy. We discuss the implications for the original model and suggest experimental systems in which a volcano transition and oscillator glass may appear.

[1]  Daido,et al.  Quasientrainment and slow relaxation in a population of oscillators with random and frustrated interactions. , 1992, Physical review letters.

[2]  Mandel,et al.  Global coupling with time delay in an array of semiconductor lasers , 2000, Physical review letters.

[3]  S. Kirkpatrick,et al.  Solvable Model of a Spin-Glass , 1975 .

[4]  A. Cavagna,et al.  Spin-glass theory for pedestrians , 2005, cond-mat/0505032.

[5]  H. Daido,et al.  Population Dynamics of Randomly Interacting Self-Oscillators. I Tractable Models without Frustration , 1987 .

[6]  A. Stefanovska,et al.  Glassy states and super-relaxation in populations of coupled phase oscillators , 2013, Nature Communications.

[7]  E. Ott,et al.  Low dimensional behavior of large systems of globally coupled oscillators. , 2008, Chaos.

[8]  Hyunsuk Hong,et al.  Mean-field behavior in coupled oscillators with attractive and repulsive interactions. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Hyunsuk Hong,et al.  Conformists and contrarians in a Kuramoto model with identical natural frequencies. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  John L Hudson,et al.  Emerging Coherence in a Population of Chemical Oscillators , 2002, Science.

[11]  J. C. Stiller,et al.  Dynamics of nonlinear oscillators with random interactions , 1998 .

[12]  Steven H. Strogatz,et al.  Dynamics of a Large Array of Globally Coupled Lasers with Distributed frequencies , 2001, Int. J. Bifurc. Chaos.

[13]  K. Showalter,et al.  Spiral wave chimera states in large populations of coupled chemical oscillators , 2017 .

[14]  M. Rosenblum,et al.  Partially integrable dynamics of hierarchical populations of coupled oscillators. , 2008, Physical review letters.

[15]  Wiesenfeld,et al.  Synchronization transitions in a disordered Josephson series array. , 1996, Physical review letters.

[16]  Daido.  Algebraic relaxation of an order parameter in randomly coupled limit-cycle oscillators , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  Hyunsuk Hong,et al.  Kuramoto model of coupled oscillators with positive and negative coupling parameters: an example of conformist and contrarian oscillators. , 2011, Physical review letters.

[18]  Isabel M. Kloumann,et al.  Phase diagram for the Kuramoto model with van Hemmen interactions. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Monika Sharma,et al.  Chemical oscillations , 2006 .

[20]  Yoshiki Kuramoto,et al.  Chemical Oscillations, Waves, and Turbulence , 1984, Springer Series in Synergetics.

[21]  Arkady Pikovsky,et al.  Dynamics of globally coupled oscillators: Progress and perspectives. , 2015, Chaos.

[22]  A. Winfree.  Biological rhythms and the behavior of populations of coupled oscillators. , 1967, Journal of theoretical biology.

[23]  Florian Marquardt,et al.  Collective dynamics in optomechanical arrays , 2010, 2013 Conference on Lasers & Electro-Optics Europe & International Quantum Electronics Conference CLEO EUROPE/IQEC.

[24]  Roy,et al.  Coherence and phase dynamics of spatially coupled solid-state lasers. , 1993, Physical review. A, Atomic, molecular, and optical physics.

[25]  E. Ott,et al.  Long time evolution of phase oscillator systems. , 2009, Chaos.

[26]  Antonio-José Almeida,et al.  NAT , 2019, Springer Reference Medizin.

[27]  Damian H. Zanette,et al.  Synchronization and frustration in oscillator networks with attractive and repulsive interactions , 2005 .

[28]  R. Sarpong,et al.  Bio-inspired synthesis of xishacorenes A, B, and C, and a new congener from fuscol† †Electronic supplementary information (ESI) available. See DOI: 10.1039/c9sc02572c , 2019, Chemical science.

[29]  Stiller,et al.  Self-averaging of an order parameter in randomly coupled limit-cycle oscillators , 2000, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.