Sequence of routes to chaos in a Lorenz-type system
type: Item
instance of: scholarly article
title: Sequence of routes to chaos in a Lorenz-type system
zbMATH Open document ID: 1448.34092
DOI: 10.1155/2020/3162170
author: Yongming Cao
author: Qingdu Li
author: Fangyan Yang
author: Lijuan Chen
published in: Discrete Dynamics in Nature and Society
publication date: 2020-07-21T00:00:00Z
review text: A new chaotic system, which is a modification of the well-known Lorenz model, is proposed. A comprehensive study of the considered system is carried out, including the study of symmetry, equilibria, stability, and nonlinear dynamics. It is shown that, depending on the parity of the number \(n\), the system can exhibit different bifurcation behavior. Moreover, in the studied Lorenz-type system, many chaotic attractors are born from limit cycles with high periods in comparison with most known chaotic systems. It is also shown that, despite the unstability of all equilibria, only self-excited attractors are observed in the experiments, which distinguishes the proposed system from the known Lorenz model with hidden attractors. The results obtained help to better study the nature and variety of the occurrence of chaos in dynamical systems.
reviewed by: Aleksandra Tutueva
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C14
Mathematics Subject Classification ID: 37D45
zbMATH DE Number: 7223632
zbMATH Keywords: Lorenz-type system
zbMATH Keywords: chaos
zbMATH Keywords: bifurcation
zbMATH Keywords: self-excited attractors
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2020/3162170
OpenAlex ID: W3001109889
Wikidata QID: Q126307879
cites work: Deterministic Nonperiodic Flow
cites work: Deterministic chaos in pendulum systems with delay
cites work: On differences and similarities in the analysis of Lorenz, Chen, and Lu systems
cites work: Hyperchaos, chaos, and horseshoe in a 4D nonlinear system with an infinite number of equilibrium points
cites work: A memristor-meminductor-based chaotic system with abundant dynamical behaviors
cites work: Dynamics of the modified \(n\)-degree Lorenz system
cites work: Period Three Implies Chaos
cites work: Differentiable dynamical systems
cites work: TOPOLOGICAL HORSESHOES AND COMPUTER ASSISTED VERIFICATION OF CHAOTIC DYNAMICS
cites work: A SIMPLE METHOD FOR FINDING TOPOLOGICAL HORSESHOES
cites work: Topological horseshoes
cites work: ON THREE-DIMENSIONAL DYNAMICAL SYSTEMS CLOSE TO SYSTEMS WITH A STRUCTURALLY UNSTABLE HOMOCLINIC CURVE. II
cites work: Diffeomorphisms with infinitely many sinks
cites work: New bifurcations in the simplest passive walking model
cites work: Bifurcation and chaos in the simple passive dynamic walking model with upper body
cites work: Period-adding bifurcation and chaos in a hybrid Hindmarsh-Rose model
cites work: Hidden attractors in dynamical systems. from hidden oscillations in Hilbert-Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits
description: scientific article; zbMATH DE number 7223632