Scrutinizing critical dynamics of reaction-diffusion models on complex networks
Wei Gou1,2,3, Jianmeng Cui1,2, Yongli Song4
1Complex Systems Research Center, Shanxi University, Taiyuan 030006, China.
Chaos (Woodbury, N.Y.)
|July 24, 2026
Summary
Researchers developed a framework to analyze critical dynamics in reaction-diffusion (RD) models on complex networks. This approach reveals how network structure and node dynamics jointly determine complex behaviors like bistability and oscillations.
Area of Science:
- Complex Systems
- Nonlinear Dynamics
- Network Science
Background:
- Reaction-diffusion (RD) processes are ubiquitous in nature and technology.
- Analyzing critical dynamics in RD models on complex networks is challenging due to high dimensionality.
Purpose of the Study:
- Develop a practical framework for computing bifurcation normal forms in RD models on networks.
- Investigate how network structure and local node dynamics influence critical behaviors.
Main Methods:
- Rigorous development of a general framework for bifurcation normal form computation.
- Derivation of normal forms for Hopf, steady-state, and Turing-Hopf bifurcations.
- Analysis of ratio-dependent predator-prey and FitzHugh-Nagumo models on complex networks.
Main Results:
- Critical dynamics are jointly determined by network structure and local node dynamics.
- Ratio-dependent predator-prey models exhibit novel bifurcations, bistability, and heterogeneous oscillations.
- FitzHugh-Nagumo models on brain networks show conventional bifurcations.
Conclusions:
- The developed framework provides a foundational tool for nonlinear analysis of RD processes on complex networks.
- Understanding critical dynamics requires considering both network topology and local kinetics.
- Network structure can lead to novel emergent behaviors in dynamical systems.
Related Concept Videos
01:11Radical Reactivity: Overview
Radicals, the highly reactive species, gain stability by undergoing three different reactions. The first reaction involves a radical-radical coupling, in which a radical combines with another radical, forming a spin‐paired molecule. The second reaction is between a radical and a spin‐paired molecule, generating a new radical and a new spin‐paired molecule. The third reaction is radical decomposition in a unimolecular reaction, forming a new radical and a spin‐paired molecule. These three...
01:09Theories of Dissolution: The Danckwerts' Model and Interfacial Barrier Model
Various dissolution theories provide insight into the factors that influence the dissolution rate. Danckwerts' Model suggests that turbulence, rather than a stagnant layer, characterizes the dissolution medium at the solid-liquid interface. In this model, the agitated solvent contains macroscopic packets that move to the interface via eddy currents, facilitating the absorption and delivery of the drug to the bulk solution. The regular replenishment of solvent packets maintains the concentration...
02:27Le Chatelier's Principle: Changing Concentration
A system at equilibrium is in a state of dynamic balance, with forward and reverse reactions taking place at equal rates. If an equilibrium system is subjected to a change in conditions that affects these reaction rates differently (a stress), then the rates are no longer equal and the system is not at equilibrium. The system will subsequently experience a net reaction in the direction of a greater rate (a shift) that will re-establish the equilibrium. This phenomenon is summarized by Le...
01:15Fundamental Mathematical Principles in Pharmacokinetics: Rate and Order of Reaction
In pharmacokinetics, the rates and order of reactions play a crucial role in understanding how the body processes drugs and help us comprehend drug absorption, distribution, metabolism, and elimination. A critical concept in pharmacokinetics is the rate constant, which quantifies the speed of a reaction. It provides valuable information about the kinetics of drug elimination. The rate constant allows us to determine the rate at which drugs are eliminated from the body.
Pharmacokinetic reactions...
Pharmacokinetic reactions...
02:26Protein Networks
An organism can have thousands of different proteins, and these proteins must cooperate to ensure the health of an organism. Proteins bind to other proteins and form complexes to carry out their functions. Many proteins interact with multiple other proteins creating a complex network of protein interactions.
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
These interactions can be represented through maps depicting protein-protein interaction networks, represented as nodes and edges. Nodes are circles that are representative of a protein,...
00:57Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models
Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...