dc.contributor.author Fyodorov, YV dc.contributor.author Khoruzhenko, BA dc.date.accessioned 2016-07-13T13:54:32Z dc.date.available 2016-07-13T13:54:32Z dc.date.issued 2016-01 dc.date.submitted 2016-06-21T10:33:38.783Z dc.identifier.citation Fyodorov, Yan V. and Boris A. Khoruzhenko, "Nonlinear Analogue Of The May−Wigner Instability Transition", Proceedings of the National Academy of Sciences, 113 (2016), 6827-6832 en_US dc.identifier.uri http://qmro.qmul.ac.uk/xmlui/handle/123456789/13478 dc.description.abstract We study a system of $N\gg 1$ degrees of freedom coupled via a smooth homogeneous Gaussian vector field with both gradient and divergence-free components. In the absence of coupling, the system is exponentially relaxing to an equilibrium with rate $\mu$. We show that, while increasing the ratio of the coupling strength to the relaxation rate, the system experiences an abrupt transition from a topologically trivial phase portrait with a single equilibrium into a topologically non-trivial regime characterised by an exponential number of equilibria, the vast majority of which are expected to be unstable. It is suggested that this picture provides a global view on the nature of the May-Wigner instability transition originally discovered by local linear stability analysis. en_US dc.description.sponsorship The research of Y.V.F. was supported by EPSRC Grant EP/J002763/1, “Insights into Disordered Landscapes via Random Matrix Theory and Statistical Mechanics.” B.A.K. thanks the Isaac Newton Institute for Mathematical Sciences for its hospitality during the program Periodic and Ergodic Spectral Problems, supported by EPSRC Grant EP/K032208/1. en_US dc.publisher PNAS en_US dc.relation.isreplacedby 123456789/16019 dc.relation.isreplacedby http://qmro.qmul.ac.uk/xmlui/handle/123456789/16019 dc.rights "The final publication is available at http://www.pnas.org/content/113/25/6827.abstract” dc.subject cond-mat.dis-nn en_US dc.subject cond-mat.dis-nn en_US dc.subject cond-mat.stat-mech en_US dc.subject math-ph en_US dc.subject math.MP en_US dc.subject nlin.AO en_US dc.subject physics.bio-ph en_US dc.subject q-bio.PE en_US dc.title Nonlinear Analogue of the May-Wigner Instability Transition en_US dc.type Article en_US dc.identifier.doi 10.1073/pnas.1601136113 pubs.author-url http://arxiv.org/abs/1509.05737v3 pubs.publisher-url http://dx.doi.org/10.1073/pnas.1601136113
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