# The Turing bifurcation in network systems: Collective patterns and single differentiated nodes

@article{Wolfrum2012TheTB, title={The Turing bifurcation in network systems: Collective patterns and single differentiated nodes}, author={Matthias Wolfrum}, journal={Physica D: Nonlinear Phenomena}, year={2012}, volume={241}, pages={1351-1357} }

## 45 Citations

Predictable topological sensitivity of Turing patterns on graphs.

- MathematicsPhysical review. E
- 2022

Reaction-diffusion systems implemented as dynamical processes on networks have recently renewed the interest in their self-organized collective patterns known as Turing patterns. We investigate the…

Snaking on Networks: From Local Solutions to Turing Patterns

- Computer Science
- 2015

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.

Theory of Turing Patterns on Time Varying Networks.

- PhysicsPhysical review letters
- 2017

The process of pattern formation for a multispecies model anchored on a time varying network is studied and a closed analytical prediction for the onset of the instability in the time dependent framework is derived.

Turing instability in reaction–diffusion models on complex networks

- Mathematics, Computer Science
- 2016

Feedback-induced stationary localized patterns in networks of diffusively coupled bistable elements

- Computer Science
- 2013

Effects of feedbacks on self-organization phenomena in networks of diffusively coupled bistable elements are investigated. For regular trees, an approximate analytical theory for localized stationary…

Turing patterns mediated by network topology in homogeneous active systems.

- Computer SciencePhysical review. E
- 2019

It is demonstrated that networks with large degree fluctuations tend to have stable patterns over the space of initial perturbations, whereas patterns in more homogenous networks are purely stochastic, and the Turing instability can be induced in any network topology by tuning the diffusion of the competing species or by altering network connectivity.

Dispersal-induced destabilization of metapopulations and oscillatory Turing patterns in ecological networks

- Environmental ScienceScientific reports
- 2014

The original analysis by Turing to networks is extended and applied to ecological metapopulations with dispersal connections between habitats, finding such oscillatory instabilities for all possible food webs with three predator or prey species.

Pattern Formation on Networks: from Localised Activity to Turing Patterns

- Computer ScienceScientific reports
- 2016

Through the application of a generalisation of dynamical systems analysis this work reveals a fundamental connection between small-scale modes of activity on networks and localised pattern formation seen throughout science, such as solitons, breathers andLocalised buckling.

A theory of pattern formation for reaction–diffusion systems on temporal networks

- Computer ScienceProceedings of the Royal Society A
- 2021

Networks have become ubiquitous in the modern scientific literature, with recent work directed at understanding ‘temporal networks’—those networks having structure or topology which evolves over…

Pattern formation in multiplex networks

- Computer ScienceScientific reports
- 2015

The theory demonstrates that the existence of such topology-driven instabilities is generic in multiplex networks, providing a new mechanism of pattern formation.

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