Global dynamics for the simplified Lorenz system model

DOI10.1016/j.amc.2015.01.122zbMath1390.34113OpenAlexW2091117631MaRDI QIDQ1635555

Fuchen Zhang, Yong Lu Shu

Publication date: 7 June 2018

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2015.01.122

zbMATH Keywords

Lyapunov stabilitynumerical simulationLorenz systemattraction domainhidden attractor

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamics induced by flows and semiflows (37C10) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (4)

Further results on ultimate bound on the trajectories of the Lorenz system ⋮ Qualitative analysis of a new Lorenz-type chaotic system and its simulation ⋮ On a model of the dynamical systems describing convective fluid motion in rotating cavity ⋮ A new type of combination synchronization among multiple chaotic systems

Cites Work

• On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
• Algorithms for finding hidden oscillations in nonlinear systems. The Aizerman and Kalman conjectures and Chua's circuits
• Localization of hidden Chua's attractors
• Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization
• Projective synchronization of fractional order chaotic system based on linear separation
• Solution and attractivity for a rational recursive sequence
• Asynchronous anti-noise hyper chaotic secure communication system based on dynamic delay and state variables switching
• Bounds for a new chaotic system and its application in chaos synchronization
• Existence criterion of homoclinic trajectories in the Glukhovsky-Dolzhansky system
• Lyapunov's direct method in the estimation of the Hausdorff dimension of attractors
• Hidden attractor in smooth Chua systems
• Solutions of rational difference systems of order two
• The Tricomi problem for the Shimizu-Morioka dynamical system
• Numerical justification of Leonov conjecture on Lyapunov dimension of Rossler attractor
• General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, Lu and Chen systems
• ON THE BOUNDNESS OF SOME SOLUTIONS OF THE LÜ SYSTEM
• HIDDEN ATTRACTORS IN DYNAMICAL SYSTEMS. FROM HIDDEN OSCILLATIONS IN HILBERT–KOLMOGOROV, AIZERMAN, AND KALMAN PROBLEMS TO HIDDEN CHAOTIC ATTRACTOR IN CHUA CIRCUITS
• The dynamical analysis of a new chaotic system and simulation
• Attraktorlokalisierung des Lorenz-Systems
• An ultimate bound on the trajectories of the Lorenz system and its applications
• Deterministic Nonperiodic Flow
• GENERATING MULTISCROLL CHAOTIC ATTRACTORS: THEORIES, METHODS AND APPLICATIONS
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