Related Experiment Video
Updated: Oct 7, 2026

In Vitro Reconstitution of Self-Organizing Protein Patterns on Supported Lipid Bilayers
Published on: July 28, 2018
An alternate mechanism for the emergence of localized oscillatory patterns in networked reaction-diffusion systems
Zhi-Chao Xue1, Xiaofeng Luo2,3, Li Li4
1Complex Systems Research Center, Shanxi University, Taiyuan 030006, China.
Abstract:
Localized oscillatory patterns, confined to finite spatial domains or subsets of nodes in a network, have been observed in cortical neurons, metacommunity ecosystems, and chemical experiments.Previous studies have shown that wave bifurcations (oscillatory Turing instabilities) in undirected networked reaction-diffusion systems can induce such localized oscillations. Here, we propose an alternative mechanism for their emergence, namely Hopf-type instabilities acting on a subcritical Turing branch. Unlike wave bifurcations, this mechanism does not require interactions amongst at least three components. We further demonstrate its robustness in both the Brusselator and FitzHugh-Nagumo models in undirected Barabási-Albert, Erd˝os-Rényi, and Watts-Strogatz networks. This work extends the universality of such patterns in networked systems and provides a theoretical foundation for the control of collective dynamical phenomena in complex systems.
Related Concept Videos
Reaction Mechanisms
For instance, the decomposition of ozone appears to follow a mechanism with two steps:
Reaction Mechanisms: The Steady-State Approximation
Multi-Step Reactions
Fast Reactions
Reaction Mechanisms: Rate-limiting Step Approximation
Temperature Dependence on Reaction Rate
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. This premise is the basis for a theory that explains many observations regarding chemical kinetics, including factors affecting reaction rates.
The collision theory is based on the postulates that (i) the reaction rate is proportional to the rate of reactant collisions, (ii) the reacting species collide in an orientation allowing contact between...
