Snaking on Networks: From Local Solutions to Turing Patterns

Nicholas McCullen; Matthias Wolfrum; Thomas Wagenknecht

Snaking on Networks: From Local Solutions to Turing Patterns

Nicholas McCullen, Matthias Wolfrum, Thomas Wagenknecht

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Abstract

The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied. The transition is investigated between the single-node solutions, studied previously [Wolfrum, Physica D (2012)], and the fully developed global activation states (so called Turing states). Numerical continuation reveals snaking bifurcations connecting different solutions, similar to those found in reaction diffusion systems on regular lattice network topologies, shedding light on the origin of the multistable “Turing' patterns reported previously [Nakao & Mikhailov, Nature 2010].

Original language	English
Publication status	Unpublished - 19 May 2015
Event	SIAM Conference on Applications of Dynamical Systems - Utah, Snowbird, USA United States Duration: 17 May 2005 → 21 Aug 2015

Conference

Conference	SIAM Conference on Applications of Dynamical Systems
Country/Territory	USA United States
City	Snowbird
Period	17/05/05 → 21/08/15

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title = "Snaking on Networks: From Local Solutions to Turing Patterns",

abstract = "The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied. The transition is investigated between the single-node solutions, studied previously [Wolfrum, Physica D (2012)], and the fully developed global activation states (so called Turing states). Numerical continuation reveals snaking bifurcations connecting different solutions, similar to those found in reaction diffusion systems on regular lattice network topologies, shedding light on the origin of the multistable “Turing' patterns reported previously [Nakao & Mikhailov, Nature 2010].",

author = "Nicholas McCullen and Matthias Wolfrum and Thomas Wagenknecht",

year = "2015",

month = may,

day = "19",

language = "English",

note = "SIAM Conference on Applications of Dynamical Systems ; Conference date: 17-05-2005 Through 21-08-2015",

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T1 - Snaking on Networks: From Local Solutions to Turing Patterns

AU - McCullen, Nicholas

AU - Wolfrum, Matthias

AU - Wagenknecht, Thomas

PY - 2015/5/19

Y1 - 2015/5/19

N2 - The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied. The transition is investigated between the single-node solutions, studied previously [Wolfrum, Physica D (2012)], and the fully developed global activation states (so called Turing states). Numerical continuation reveals snaking bifurcations connecting different solutions, similar to those found in reaction diffusion systems on regular lattice network topologies, shedding light on the origin of the multistable “Turing' patterns reported previously [Nakao & Mikhailov, Nature 2010].

AB - The emergence of patterns of activity on complex networks with reaction-diffusion dynamics on the nodes is studied. The transition is investigated between the single-node solutions, studied previously [Wolfrum, Physica D (2012)], and the fully developed global activation states (so called Turing states). Numerical continuation reveals snaking bifurcations connecting different solutions, similar to those found in reaction diffusion systems on regular lattice network topologies, shedding light on the origin of the multistable “Turing' patterns reported previously [Nakao & Mikhailov, Nature 2010].

UR - http://meetings.siam.org/sess/dsp_talk.cfm?p=69962

M3 - Poster

T2 - SIAM Conference on Applications of Dynamical Systems

Y2 - 17 May 2005 through 21 August 2015

ER -

Snaking on Networks: From Local Solutions to Turing Patterns

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