ULTIMATE BOUND ESTIMATION OF A CLASS OF HIGH DIMENSIONAL QUADRATIC AUTONOMOUS DYNAMICAL SYSTEMS

DOI10.1142/S0218127411030027zbMath1248.34084OpenAlexW2154488655MaRDI QIDQ3165857

Jinhu Lü, Xinghuo Yu, Damei Li, Pei Wang, Xiao-Qun Wu

Publication date: 19 October 2012

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

Full work available at URL: https://doi.org/10.1142/s0218127411030027

zbMATH Keywords

optimizationchaosultimate bound estimationhigh dimensional quadratic autonomous systems

Mathematics Subject Classification ID

Growth and boundedness of solutions to ordinary differential equations (34C11) Complex behavior and chaotic systems of ordinary differential equations (34C28) Attractors of solutions to ordinary differential equations (34D45)

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Cites Work

• Multi-wing hyperchaotic attractors from coupled Lorenz systems
• Some synchronization strategies for a four-scroll chaotic system
• Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz-Haken system
• A constructive proof on the existence of globally exponentially attractive set and positive invariant set of general Lorenz family
• On the study of globally exponentially attractive set of a general chaotic system
• Bounds of the hyper-chaotic Lorenz-Stenflo system
• Localization of invariant compact sets of nonautonomous systems
• Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system
• A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system
• Harmonic balance methods for the analysis of chaotic dynamics in nonlinear systems
• Estimating the bounds for the Lorenz family of chaotic systems
• Globally exponentially attractive sets of the family of Lorenz systems
• Localization of invariant compact sets of dynamical systems
• A general multiscroll Lorenz system family and its realization via digital signal processors
• Attraktorlokalisierung des Lorenz-Systems
• A nine-dimensional Lorenz system to study high-dimensional chaos
• BIFURCATION AND PREDICTABILITY ANALYSIS OF A LOW-ORDER ATMOSPHERIC CIRCULATION MODEL
• An ultimate bound on the trajectories of the Lorenz system and its applications
• YET ANOTHER CHAOTIC ATTRACTOR
• Theoretical Design and Circuit Implementation of Multidirectional Multi-Torus Chaotic Attractors
• Deterministic Nonperiodic Flow
• A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM
• ON A GENERALIZED LORENZ CANONICAL FORM OF CHAOTIC SYSTEMS
• BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM
• A NEW CHAOTIC ATTRACTOR COINED
• A NOVEL HYPERCHAOTIC SYSTEM AND ITS COMPLEX DYNAMICS
• GENERATING MULTISCROLL CHAOTIC ATTRACTORS: THEORIES, METHODS AND APPLICATIONS