Graph-based topological approximation of saddle-node bifurcation in maps : Dedicated to Professor Yasumasa Nishiura for his sixtieth birthday (Far-From-Equilibrium Dynamics)
Year: 2012
Type: article
Abstract: An efficient computational framework for obtaining a rigorous combinatorial de- scription of the global dynamics over a large range of parameter values of multiparam- eter nonlinear systems was presented in [1].Because the resulting information is easily queryable and provides important information about the qualitative dynamics, we refer to the output as a database for the dynamics.Such a procedure can only involve a fi- nite number of computations and thus the dynamics can only be represented down to a fixed scale.However, the theory of dynamical systems indicates that nonlinear systems can exhibit different structures at all scales in phase space and that bifurcations of the
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funders: National Science Foundation, U.S. Department of Energy, Conselho Nacional de Desenvolvimento Científico e Tecnológico, Defense Advanced Research Projects Agency, Japan Society for the Promotion of Science, Core Research for Evolutional Science and Technology, Air Force Office of Scientific Research
Awards: Analysis of the global structure of chaotic dynamical systems by topological and computational methods, G1617213867, Dynamics and synchronization of biochemical oscillators, CDI-Type II: Collaborative Research: Computational Homology, Jamming, and Force Chains in Dense Granular Flows, G222768804, G2581719517, Collaborative proposal: Computing Dynamics of Multiparameter Systems, Toward a new approach to transient dynamics, MULTISCALE ANALYSIS OF NONLINEAR SYSTEMS USING COMPUTATIONAL TOPOLOGY, MULTISCALE ANALYSIS OF NONLINEAR SYSTEMS USING COMPUTATIONAL TOPOLOGY, Collaborative Research: Topological Methods for the Study of Nonlinear Infinite Dimensional Systems
OpenAlex ID: W1562289331