Research output: Contribution to journal › Article

**Nonlinear analogue of the May−Wigner instability transition.** / Fyodorov, Yan V.; Khoruzhenko, Boris A.

Research output: Contribution to journal › Article

Fyodorov, YV & Khoruzhenko, BA 2016, 'Nonlinear analogue of the May−Wigner instability transition', *PNAS*, vol. 113, no. 25, pp. 6827–6832. https://doi.org/10.1073/pnas.1601136113

Fyodorov, Y. V., & Khoruzhenko, B. A. (2016). Nonlinear analogue of the May−Wigner instability transition. *PNAS*, *113*(25), 6827–6832. https://doi.org/10.1073/pnas.1601136113

Fyodorov YV, Khoruzhenko BA. Nonlinear analogue of the May−Wigner instability transition. PNAS. 2016 Jun;113(25):6827–6832. https://doi.org/10.1073/pnas.1601136113

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title = "Nonlinear analogue of the May−Wigner instability transition",

abstract = "We study a system of N 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 µ. 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.",

author = "Fyodorov, {Yan V.} and Khoruzhenko, {Boris A.}",

year = "2016",

month = "6",

doi = "10.1073/pnas.1601136113",

language = "English",

volume = "113",

pages = "6827–6832",

journal = "Proceedings of the National Academy of Sciences of the United States of America",

issn = "0027-8424",

publisher = "National Acad Sciences",

number = "25",

}

TY - JOUR

T1 - Nonlinear analogue of the May−Wigner instability transition

AU - Fyodorov, Yan V.

AU - Khoruzhenko, Boris A.

PY - 2016/6

Y1 - 2016/6

N2 - We study a system of N 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 µ. 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.

AB - We study a system of N 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 µ. 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.

U2 - 10.1073/pnas.1601136113

DO - 10.1073/pnas.1601136113

M3 - Article

VL - 113

SP - 6827

EP - 6832

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 25

ER -

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