Ultimate bound of a 3D chaotic system and its application in chaos synchronization
type: Item
instance of: scholarly article
title: Ultimate bound of a 3D chaotic system and its application in chaos synchronization
zbMATH Open document ID: 1406.93137
DOI: 10.1155/2014/781594
author: Jiezhi Wang
author: Qing Zhang
author: Hang Li
author: Zengqiang Chen
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Two ellipsoidal ultimate boundary regions of a special three-dimensional (3D) chaotic system are proposed. To this chaotic system, the linear coefficient of the \(i\)th state variable in the \(i\)th state equation has the same sign; it also has two one-order terms and one quadratic cross-product term in each equation. A numerical solution and an analytical expression of the ultimate bounds are received. To get the analytical expression of the ultimate boundary region, a new result of one maximum optimization question is proved. The corresponding ultimate boundary regions are demonstrated through numerical simulations. Utilizing the bounds obtained, a linear controller is proposed to achieve the complete chaos synchronization. Numerical simulation exhibits the feasibility of the designed scheme.
Mathematics Subject Classification ID: 93C05
Mathematics Subject Classification ID: 93C10
Mathematics Subject Classification ID: 93C15
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7023052
zbMATH Keywords: 3D chaotic system
zbMATH Keywords: chaos synchronization
zbMATH Keywords: ultimate boundary region
zbMATH Keywords: linear controller
Wikidata QID: Q59041390
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/781594
OpenAlex ID: W2155622857
cites work: Estimating the ultimate bound and positively invariant set for a new chaotic system and its application in chaos synchronization
cites work: Bounds for a new chaotic system and its application in chaos synchronization
cites work: Chaotic control and generalized synchronization for a hyperchaotic Lorenz-Stenflo system
cites work: Deterministic Nonperiodic Flow
cites work: Q3817333
cites work: Attraktorlokalisierung des Lorenz-Systems
cites work: An ultimate bound on the trajectories of the Lorenz system and its applications
cites work: Estimating the bounds for the Lorenz family of chaotic systems
cites work: On the new results of global attractive set and positive invariant set of the Lorenz chaotic system and the applications to chaos control and synchronization
cites work: Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system
cites work: Globally exponentially attractive sets of the family of Lorenz systems
cites work: A butterfly-shaped localization set for the Lorenz attractor
cites work: GLOBALLY ATTRACTIVE AND POSITIVE INVARIANT SET OF THE LORENZ SYSTEM
cites work: NEW ESTIMATIONS FOR GLOBALLY ATTRACTIVE AND POSITIVE INVARIANT SET OF THE FAMILY OF THE LORENZ SYSTEMS
cites work: Q4787056
cites work: BRIDGE THE GAP BETWEEN THE LORENZ SYSTEM AND THE CHEN SYSTEM
cites work: YET ANOTHER CHAOTIC ATTRACTOR
cites work: A NEW CHAOTIC ATTRACTOR COINED
cites work: On the boundedness of solutions of the Chen system
cites work: On the boundness of some solutions of the Lü system
cites work: On the boundedness of solutions to the Lorenz-like family of chaotic systems
cites work: On the study of globally exponentially attractive set of a general chaotic system
cites work: GLOBAL ANALYSIS ON n-SCROLL CHAOTIC ATTRACTORS OF MODIFIED CHUA'S CIRCUIT
cites work: Localization of hidden Chua's attractors
cites work: Estimating the ultimate bound and positively invariant set for the hyperchaotic Lorenz-Haken system
cites work: Bounds of the hyper-chaotic Lorenz-Stenflo system
cites work: A novel bounded 4D chaotic system
cites work: ULTIMATE BOUND ESTIMATION OF A CLASS OF HIGH DIMENSIONAL QUADRATIC AUTONOMOUS DYNAMICAL SYSTEMS
cites work: A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM
description: scientific article; zbMATH DE number 7023052