Computational chaos - a prelude to computational instability
From MaRDI portal
Publication:920269
DOI10.1016/0167-2789(89)90072-9zbMath0708.34043OpenAlexW1996473620MaRDI QIDQ920269
Publication date: 1989
Published in: Physica D (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0167-2789(89)90072-9
Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Numerical methods for ordinary differential equations (65L99)
Related Items
On the risks of using double precision in numerical simulations of spatio-temporal chaos, A kind of Lagrangian chaotic property of the Arnold–Beltrami–Childress flow, On noninvertible mappings of the plane: Eruptions, Global bifurcations in Rayleigh-Bénard convection. Experiments, empirical maps and numerical bifurcation analysis, Stability of artificial neural networks with impulses, Difference equations versus differential equations, a possible equivalence for the Rössler system?, Clean numerical simulation: a new strategy to obtain reliable solutions of chaotic dynamic systems, The Lorenz model in discrete time, Synchronization between the spatial Julia sets of complex Lorenz system and complex Henon map, The dynamics of a fold-and-twist map, Spectral element methods for nonlinear spatio-temporal dynamics of an Euler-Bernoulli beam, Some historical aspects of nonlinear dynamics -- possible trends for the future, Computation of the largest positive Lyapunov exponent using rounding mode and recursive least square algorithm, Can We Obtain a Reliable Convergent Chaotic Solution in any Given Finite Interval of Time?, Influence of the Integration Steps on the Results of Numerical Simulations for a System with Friction, On the analysis of pseudo-orbits of continuous chaotic nonlinear systems simulated using discretization schemes in a digital computer, Chaos in planar oscillations of a Toda particle, A COMPUTER-ASSISTED STUDY OF GLOBAL DYNAMIC TRANSITIONS FOR A NONINVERTIBLE SYSTEM, Torus destruction in a nonsmooth noninvertible map, A Self-Adaptive Algorithm of the Clean Numerical Simulation (CNS) for Chaos, On the susceptibility of numerical methods to computational chaos and superstability, Discrete chaos in a novel two-dimensional fractional chaotic map, FROM SYMMETRY TO COMPLEXITY: ON INSTABILITIES AND THE UNITY IN DIVERSITY IN NONLINEAR SCIENCE, Homoclinic Orbits and Solitary Waves within the Nondissipative Lorenz Model and KdV Equation, Dynamical approach study of spurious steady-state numerical solutions of nonlinear differential equations. I: The dynamics of time discretization and its implications for algorithm development in computational fluid dynamics, An adaptation of Adomian decomposition for numeric-analytic integration of strongly nonlinear and chaotic oscillators, A semi‐analytical locally transversal linearization method for non‐linear dynamical systems, The structure of synchronization sets for noninvertible systems, Periodicity and Chaos Amidst Twisting and Folding in Two-Dimensional Maps, Qualitative properties and two strong resonances of a discrete reduced Lorenz system, On Reliable Computation of Lifetime in Transient Chaos, Defect-controlled numerical methods and shadowing for chaotic differential equations, Algebraic calculation of stroboscopic maps of ordinary, nonlinear differential equations, Bifurcation analysis and chaos in a discrete reduced Lorenz system, A multistep transversal linearization (MTL) method in nonlinear dynamics through a Magnus characterization, On the noise-perturbed spatial Julia set generated by Lorenz system, Qualitative properties and bifurcations of a leaf-eating herbivores model, Chaos and fractal properties induced by noninvertibility of models in the form of maps, Spectral element methods for nonlinear temporal dynamical systems, Numerical Dynamics of Ordinary Differential Equations with Singularity, Novel routes to chaos through torus breakdown in non-invertible maps, Physical limit of prediction for chaotic motion of three-body problem, Computational Complex Dynamcs of the Discrete Lorenz System, Classification of critical sets and their images for quadratic maps of the plane, Detecting unreliable computer simulations of recursive functions with interval extensions, Invariant sets and attractors of quadratic mapping of plane: Computer experiment and analytical treatment, Algorithms for controlling chaotic motion: Application for the BVP oscillator, A route to computational chaos revisited: Noninvertibility and the breakup of an invariant circle, Parameterized stable/unstable manifolds for periodic solutions of implicitly defined dynamical systems
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- On the iteration of a rational function: Computer experiments with Newton's method
- Chaos in numerical analysis of ordinary differential equations
- Central difference scheme and chaos
- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- A two-dimensional mapping with a strange attractor
- A chaotic mapping that displays its own homoclinic structure
- Euler's finite difference scheme and chaos
- On the abundance of aperiodic behaviour for maps on the interval
- On the bifurcation of maps of the interval
- Period Three Implies Chaos
- Deterministic Nonperiodic Flow
