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  • Mar
    2

    Rennie Mirollo: Is the Ott-Antonsen Manifold Attracting?

    McCormick-Engineering Sciences and Applied Mathematics

    4:00 PM M416, Technological Institute

    EVENT DETAILS

    Title: Is the Ott-Antonsen Manifold Attracting?

    Speaker: Rennie Mirollo, Ph.D., Boston College

    Abstract: The Kuramoto model is a paradigm for studying oscillator networks with interplay between coupling tending towards synchronization, and heterogeneity in the oscillator population driving away from synchrony. In continuum versions of this model, an oscillator population is represented by a probability density on the circle. In 2007, Ott and Antonsen identified a special class of densities which is invariant under the dynamics, and for which the dynamics are low-dimensional and analytically tractable. The reduction to this so-called OA manifold has been used to analyze the dynamics of many variants of the Kuramoto model. We will address the fundamental question of whether the OA manifold is attracting in the full state space. We show that for models with a finite number of populations, the OA manifold is not attracting in any sense; moreover, the dynamical behavior off the OA manifold is typically more complicated than on the OA manifold.

    The OA manifold consists of Poisson densities; a simple extension of the OA manifold consists of averages of pairs of Poisson densities. We prove that the hyperbolic distance in the disc between the centroids of each Poisson pair is a dynamical invariant. These conserved quantities, defined on the double Poisson manifold, give a way to measure the distance to the OA manifold, and this metric is dynamically invariant. This invariance implies that the OA manifold is not attracting. As an application, we show that chimera states, in which some but not all oscillator populations are in sync, can never be stable in the full state space, even if stable within the OA manifold. More importantly, perturbations of chimera states will have more complex dynamics off the OA manifold; for example, perturbing from a chimera state which is stable in the OA will yield limit cycle dynamics, and perturbing from a periodic chimera state stable in the OA (“breathing chimera”) will yield quasi-periodic dynamics. More generally, this framework allows for the analysis of multi-population continuum Kuramoto networks beyond the OA manifold, with the potential to reveal more intricate dynamical behavior than has previously been observed for these networks.

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    TIME Monday, March 2, 2020 at 4:00 PM - 5:00 PM

    LOCATION M416, Technological Institute    map it

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    CONTACT Meelee Ahn Park    meelee.park@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics

  • Apr
    23

    Appl Math: Tom Dean on "Contrail Climate Impacts: Modeling and Mitigation Strategies"

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

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    TIME Tuesday, April 23, 2024 at 11:15 AM - 12:15 PM

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    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • Apr
    30

    Appl Math: Ehud Yariv on "Shocks and Caps in Drop Electrohydrodynamics"

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

    EVENT DETAILS

    TIME Tuesday, April 30, 2024 at 11:15 AM - 12:15 PM

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    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • May
    7

    Appl Math: Pankaj Mehta on "Mathematics of Life Seminar Series: Randomness, Complexity, and the Biological Frontier"

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

    EVENT DETAILS

    TIME Tuesday, May 7, 2024 at 11:15 AM - 12:15 PM

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    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • May
    8

    Extending Care: A Conversation about Conservation and Futurity

    Block Museum of Art

    6:00 PM Block Museum of Art, Mary and Leigh

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    TIME Wednesday, May 8, 2024 at 6:00 PM - 7:30 PM

    LOCATION Block Museum of Art, Mary and Leigh    map it

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    CONTACT Block Museum of Art    block-museum@northwestern.edu EMAIL

    CALENDAR Block Museum of Art

  • May
    14

    Appl Math: Rony Granek on "Active Fractal Networks with Stochastic Force Monopoles and Force Dipoles Unravel Subdiffusion of Chromosomal Loci"

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

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    TIME Tuesday, May 14, 2024 at 11:15 AM - 12:15 PM

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    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • May
    21

    Appl Math: Andrew Stuart on "Title TBA"

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

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    TIME Tuesday, May 21, 2024 at 11:15 AM - 12:15 PM

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    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • May
    28

    Appl Math: Pascale Garaud on "Title TBA"

    McCormick-Engineering Sciences and Applied Mathematics (ESAM)

    11:15 AM M416, Technological Institute

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    TIME Tuesday, May 28, 2024 at 11:15 AM - 12:15 PM

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    CONTACT Ted Shaeffer    ted.shaeffer@northwestern.edu EMAIL

    CALENDAR McCormick-Engineering Sciences and Applied Mathematics (ESAM)

  • Jun
    10

    Northwestern Engineering PhD Hooding and Master's Degree Recognition Ceremony

    McCormick School of Engineering and Applied Science

    9:00 AM Welsh-Ryan Arena

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    TIME Monday, June 10, 2024 at 9:00 AM - 11:00 AM

    LOCATION Welsh-Ryan Arena   

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    CONTACT Amy Pokrass    amy.pokrass@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science

  • Jun
    10

    Northwestern Engineering Undergraduate Convocation

    McCormick School of Engineering and Applied Science

    2:00 PM Welsh-Ryan Arena

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    TIME Monday, June 10, 2024 at 2:00 PM - 4:00 PM

    LOCATION Welsh-Ryan Arena   

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    CONTACT Amy Pokrass    amy.pokrass@northwestern.edu EMAIL

    CALENDAR McCormick School of Engineering and Applied Science