An algorithm to automatically detect the Smale horseshoes

DOI10.1155/2012/283179zbMath1253.37005OpenAlexW2063055007WikidataQ58700449 ScholiaQ58700449MaRDI QIDQ444246

Qingdu Li, Li-Na Zhang, Fang-Yan Yang

Publication date: 14 August 2012

Published in: Discrete Dynamics in Nature and Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2012/283179

zbMATH Keywords

chaotic dynamicsalgorithms for finding Smale horseshoesSmale horseschoe

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04)

Related Items (8)

Topological Horseshoe Analysis, Ultimate Boundary Estimations of a New 4D Hyperchaotic System and Its FPGA Implementation ⋮ Computing Complex Horseshoes by Means of Piecewise Maps ⋮ Bifurcation and chaos in the simple passive dynamic walking model with upper body ⋮ Horseshoe chaos in a 3D neural network with different activation functions ⋮ Bifurcation and chaotic behavior of a discrete-time SIS model ⋮ Hyperchaos, chaos, and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points ⋮ Ultimate boundary estimations and topological horseshoe analysis of a new 4D hyper-chaotic system ⋮ Ultimate boundary estimation and topological horseshoe analysis on a parallel 4D hyperchaotic system with any number of attractors and its multi-scroll

Uses Software

• AUTO

Cites Work

• A computer-assisted proof of chaos in Josephson junctions
• A two-dimensional mapping with a strange attractor
• Growing 1D and quasi-2D unstable manifolds of maps
• Covering relations for multidimensional dynamical systems
• A 3D Smale horseshoe in a hyperchaotic discrete-time system
• Topological horseshoes
• A planar topological horseshoe theory with applications to computer verifications of chaos
• HYPERCHAOS IN A SPACECRAFT POWER SYSTEM
• TOPOLOGICAL HORSESHOES AND COMPUTER ASSISTED VERIFICATION OF CHAOTIC DYNAMICS
• OPTIMIZATION AND THE MIRANDA APPROACH IN DETECTING HORSESHOE-TYPE CHAOS BY COMPUTER
• A SIMPLE METHOD FOR FINDING TOPOLOGICAL HORSESHOES
• Introduction to Applied Nonlinear Dynamical Systems and Chaos

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