Snaking on Networks: From Local Solutions to Turing Patterns

Nicholas McCullen, Matthias Wolfrum, Thomas Wagenknecht

Research output: Contribution to conferencePoster

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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 languageEnglish
Publication statusUnpublished - 19 May 2015
EventSIAM Conference on Applications of Dynamical Systems - Utah, Snowbird, USA United States
Duration: 17 May 200521 Aug 2015

Conference

ConferenceSIAM Conference on Applications of Dynamical Systems
CountryUSA United States
CitySnowbird
Period17/05/0521/08/15

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lateral oscillation
topology
activation

Cite this

McCullen, N., Wolfrum, M., & Wagenknecht, T. (2015). Snaking on Networks: From Local Solutions to Turing Patterns. Poster session presented at SIAM Conference on Applications of Dynamical Systems, Snowbird, USA United States.

Snaking on Networks: From Local Solutions to Turing Patterns. / McCullen, Nicholas; Wolfrum, Matthias; Wagenknecht, Thomas.

2015. Poster session presented at SIAM Conference on Applications of Dynamical Systems, Snowbird, USA United States.

Research output: Contribution to conferencePoster

McCullen, N, Wolfrum, M & Wagenknecht, T 2015, 'Snaking on Networks: From Local Solutions to Turing Patterns', SIAM Conference on Applications of Dynamical Systems, Snowbird, USA United States, 17/05/05 - 21/08/15.
McCullen N, Wolfrum M, Wagenknecht T. Snaking on Networks: From Local Solutions to Turing Patterns. 2015. Poster session presented at SIAM Conference on Applications of Dynamical Systems, Snowbird, USA United States.
McCullen, Nicholas ; Wolfrum, Matthias ; Wagenknecht, Thomas. / Snaking on Networks: From Local Solutions to Turing Patterns. Poster session presented at SIAM Conference on Applications of Dynamical Systems, Snowbird, USA United States.
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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].

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