scholarly journals Dynamical analysis of a new chaotic system and its chaotic control

2007 ◽  
Vol 56 (11) ◽  
pp. 6230
Author(s):  
Cai Guo-Liang ◽  
Tan Zhen-Mei ◽  
Zhou Wei-Huai ◽  
Tu Wen-Tao
Keyword(s):  
Chaotic System ◽  
Dynamical Analysis ◽  
Chaotic Control ◽  
New Chaotic System

scholarly journals Dynamical Analysis and Periodic Solution of a Chaotic System with Coexisting Attractors

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Mingshu Chen ◽  
Zhen Wang ◽  
Xiaojuan Zhang ◽  
Huaigu Tian
Keyword(s):  
Chaotic System ◽  
Vector Fields ◽  
Dynamical Analysis ◽  
Stable Node ◽  
Polynomial Vector Fields ◽  
Coexisting Attractors ◽  
Poincaré Compactification ◽  
Unstable Node ◽  
New Chaotic System ◽  
Multiple Coexisting Attractors

Chaotic attractors with no equilibria, with an unstable node, and with stable node-focus are presented in this paper. The conservative solutions are investigated by the semianalytical and seminumerical method. Furthermore, multiple coexisting attractors are investigated, and circuit is carried out. To study the system’s global structure, dynamics at infinity for this new chaotic system are studied using Poincaré compactification of polynomial vector fields in R 3 . Meanwhile, the dynamics near the infinity of the singularities are obtained by reducing the system’s dimensions on a Poincaré ball. The averaging theory analyzes the periodic solution’s stability or instability that bifurcates from Hopf-zero bifurcation.

scholarly journals Dynamical Analysis and Simulation of a New Lorenz-Like Chaotic System

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
You Li ◽  
Ming Zhao ◽  
Fengjie Geng
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Heteroclinic Orbits ◽  
Dynamical Analysis ◽  
Poincaré Compactification ◽  
Stable And Unstable Manifolds ◽  
Dynamical Behaviors ◽  
New Chaotic System ◽  
New Type

This work presents and investigates a new chaotic system with eight terms. By numerical simulation, the two-scroll chaotic attractor is found for some certain parameters. And, by theoretical analysis, we discuss the dynamical behavior of the new-type Lorenz-like chaotic system. Firstly, the local dynamical properties, such as the distribution and the local stability of all equilibrium points, the local stable and unstable manifolds, and the Hopf bifurcations, are all revealed as the parameters varying in the space of parameters. Secondly, by applying the way of Poincaré compactification in ℝ 3 , the dynamics at infinity are clearly analyzed. Thirdly, combining the dynamics at finity and those at infinity, the global dynamical behaviors are formulated. Especially, we have proved the existence of the infinite heteroclinic orbits. Furthermore, all obtained theoretical results in this paper are further verified by numerical simulations.

The dynamical analysis of a new chaotic system and simulation

2013 ◽  
Vol 37 (12) ◽  
pp. 1838-1846 ◽  
Author(s):  
Fuchen Zhang ◽  
Chunlai Mu ◽  
Pan Zheng ◽  
Da Lin ◽  
Guangyun Zhang
Keyword(s):  
Chaotic System ◽  
Dynamical Analysis ◽  
New Chaotic System

scholarly journals The dynamics of a new chaotic system through the Caputo–Fabrizio and Atanagan–Baleanu fractional operators

2019 ◽  
Vol 11 (7) ◽  
pp. 168781401986654 ◽  
Author(s):  
Muhammad Altaf Khan
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Order Parameter ◽  
Numerical Procedure ◽  
Numerical Approach ◽  
Fractional Operators ◽  
Fundamental Properties ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Model Apply

The aim of this article is to analyze the dynamics of the new chaotic system in the sense of two fractional operators, that is, the Caputo–Fabrizio and the Atangana–Baleanu derivatives. Initially, we consider a new chaotic model and present some of the fundamental properties of the model. Then, we apply the Caputo–Fabrizio derivative and implement a numerical procedure to obtain their graphical results. Further, we consider the same model, apply the Atangana–Baleanu operator, and present their analysis. The Atangana–Baleanu model is used further to present a numerical approach for their solutions. We obtain and discuss the graphical results to each operator in details. Furthermore, we give a comparison of both the operators applied on the new chaotic model in the form of various graphical results by considering many values of the fractional-order parameter [Formula: see text]. We show that at the integer case, both the models (in Caputo–Fabrizio sense and the Atangana–Baleanu sense) give the same results.

A HYPERCHAOTIC SYSTEM WITH A FOUR-WING ATTRACTOR

2009 ◽  
Vol 20 (02) ◽  
pp. 323-335 ◽  
Author(s):  
GUOSI HU ◽  
BO YU
Keyword(s):  
System Dynamics ◽  
Lyapunov Exponents ◽  
Computer Simulations ◽  
Chaotic System ◽  
Bifurcation Analysis ◽  
Topological Structure ◽  
Hyperchaotic System ◽  
Wide Range ◽  
New Chaotic System

Recently, there are many methods for constructing multi-wing/multi-scroll or hyperchaotic attractors; however, it has been noticed that the attractors with both multi-wing topological structure and hyperchaotic characteristic rarely exist. A new chaotic system, obtained by making the change on coordinate to the Hu chaotic system, can generate very complex attractors with four-wing topological structure and three positive Lyapunov exponents over a wide range of parameters. The influence of parameters varying to system dynamics is analyzed, computer simulations and bifurcation analysis is also verified in this paper.

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