A New Reliable Numerical Method for Computing Chaotic Solutions of Dynamical Systems: The Chen Attractor Case

DOI10.1142/S0218127415501874zbMath1330.37069OpenAlexW2226191106MaRDI QIDQ5744118

Alexander N. Pchelintsev, René Lozi

Publication date: 17 February 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127415501874

zbMATH Keywords

power seriesPoisson stabilityregion of convergenceChen attractorrecurrent trajectory

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Simulation of dynamical systems (37M05) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Numerical methods for ordinary differential equations (65L99)

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An Accurate Numerical Method and Algorithm for Constructing Solutions of Chaotic Systems ⋮ A true three-scroll chaotic attractor coined ⋮ A new accurate numerical method of approximation of chaotic solutions of dynamical model equations with quadratic nonlinearities ⋮ Homoclinic Bifurcations and Chaos in the Fishing Principle for the Lorenz-like Systems ⋮ Cryptanalysis of a Classical Chaos-Based Cryptosystem with Some Quantum Cryptography Features ⋮ Analysis of chaotic behavior of three-dimensional dynamical systems by a B-spline differential quadrature algorithm

Uses Software

• MPFR
• RODES

Cites Work

• Can we trust in numerical computations of chaotic solutions of dynamical systems ?
• Solving Ordinary Differential Equations I
• YET ANOTHER CHAOTIC ATTRACTOR
• Numerical and physical modeling of the dynamics of the Lorenz system
• BIFURCATION ANALYSIS OF CHEN'S EQUATION
• Unnamed Item
• Unnamed Item

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