Dynamics of complex heterogeneous networks: reduction techniques
Dynamical phenomena in complex networks: fundamentals and applications
Probabilistic and algebraic aspects of smooth dynamical systems
Grant number: | 21/11091-3 |
Support type: | Scholarships abroad - Research Internship - Doctorate |
Effective date (Start): | December 20, 2021 |
Effective date (End): | December 19, 2022 |
Field of knowledge: | Physical Sciences and Mathematics - Mathematics - Applied Mathematics |
Principal researcher: | Tiago Pereira da Silva |
Grantee: | Zheng Bian |
Supervisor abroad: | Jeroen Steven Willibrord Lamb |
Home Institution: | Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil |
Research place: | Imperial College London, England |
Associated to the scholarship: | 18/26107-0 - Dynamics of complex heterogeneous networks: reduction techniques, BP.DR |
Abstract This proposal aims to develop a rigorous dimension reduction principle for dynamical systems coupled on complex networks by comparing the low-degree-node dynamics against a reference random dynamical system (RDS). A recent breakthrough due to Pereira, van Strien, and Tanzi proved the dimension reduction for a special class of heterogeneously coupled maps, relying crucially on global hyperbolicity properties of the network dynamics. In particular, this means that their result does not apply in power-law graphs, which constitute important examples of real-world networks. Our strategy removes the restrictive conditions of global hyperbolicity, and introduces noise to dynamics on the low-degree nodes. Specifically, we propose the following objectives.1- Merge a probabilistic argument and a topological one.2- Large-scale numerics for heterogeneously coupled hyperbolic systems.These objectives will, on the one hand, significantly extend the dimension reduction results to realistic networks including power-law and hierarchical graph models, and on the other hand, pro- vide theoretical framework for applications including reconstruction problems where the isolated dynamics are high-dimensional and possess both expanding and contracting directions. | |
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