Topological conjugacy of discrete time-map and Euler discrete dynamical systems generated by a gradient flow on a two-dimensional compact manifold

DOI10.1016/S0362-546X(01)00896-3zbMath1015.37017OpenAlexW2007348543WikidataQ123956612 ScholiaQ123956612MaRDI QIDQ1849037

Andrzej Bielecki

Publication date: 28 November 2002

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0362-546x(01)00896-3

zbMATH Keywords

gradient flowtopological conjugacyEuler method

Mathematics Subject Classification ID

Learning and adaptive systems in artificial intelligence (68T05) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25)

Related Items (5)

Topological dynamic consistency of numerical methods for dynamical models in biosciences ⋮ Bifurcation and chaos in a discrete-time predator-prey system of Holling and Leslie type ⋮ Dynamical properties of a perceptron learning process: structural stability under numerics and shadowing ⋮ Shadowing property in analysis of neural networks dynamics. ⋮ EFFECT OF STEP SIZE ON BIFURCATIONS AND CHAOS OF A MAP-BASED BVP OSCILLATOR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A proof of the \(C^ 1\) stability conjecture
• Discretized ordinary differential equations and the Conley index
• Topological invariants and detection of periodic orbits
• On invariant closed curves for one-step methods
• On structural stability of ordinary differential equations with respect to discretization methods
• Asymptotic Behavior of Stable Manifolds
• Center manifolds of dynamical systems under discretization
• On the Numerical Approximation of Phase Portraits Near Stationary Points
• Discretization in the Method of Averaging
• On the qualitative behavior of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point
• Structural Stability of Morse--Smale Gradient-like Flows under Discretizations
• The discretized flow on domains of attraction: a structural stability result
• Topological conjugacy of cascades generated by gradient flows on the two-dimensional sphere
• Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
• On C^j-closeness between the solution flow and its numerical approximation
• Dynamical properties of learning process of weakly nonlinear and nonlinear neurons

This page was built for publication: Topological conjugacy of discrete time-map and Euler discrete dynamical systems generated by a gradient flow on a two-dimensional compact manifold