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.

Various Types of Coexisting Attractors in a New 4D Autonomous Chaotic System

2017 ◽  
Vol 27 (09) ◽  
pp. 1750142 ◽  
Author(s):  
Qiang Lai ◽  
Akif Akgul ◽  
Xiao-Wen Zhao ◽  
Huiqin Pei
Keyword(s):  
Numerical Simulation ◽  
Dynamic Behavior ◽  
Chaotic System ◽  
Limit Cycles ◽  
Electronic Circuit ◽  
Strange Attractors ◽  
Bifurcation Diagrams ◽  
Coexisting Attractors ◽  
Signum Function ◽  
Multiple Coexisting Attractors

An unique 4D autonomous chaotic system with signum function term is proposed in this paper. The system has four unstable equilibria and various types of coexisting attractors appear. Four-wing and four-scroll strange attractors are observed in the system and they will be broken into two coexisting butterfly attractors and two coexisting double-scroll attractors with the variation of the parameters. Numerical simulation shows that the system has various types of multiple coexisting attractors including two butterfly attractors with four limit cycles, two double-scroll attractors with a limit cycle, four single-scroll strange attractors, four limit cycles with regard to different parameters and initial values. The coexistence of the attractors is determined by the bifurcation diagrams. The chaotic and hyperchaotic properties of the attractors are verified by the Lyapunov exponents. Moreover, we present an electronic circuit to experimentally realize the dynamic behavior of the system.

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 FPGA implementation of a large range chaotic system with coexisting attractors

2018 ◽  
Vol 11 ◽  
pp. 368-376 ◽  
Author(s):  
Yong-ju Xian ◽  
Cheng Xia ◽  
Tao-tao Guo ◽  
Kun-rong Fu ◽  
Chang-biao Xu
Keyword(s):  
Chaotic System ◽  
Large Range ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Coexisting Attractors

AN UNUSUAL 3D AUTONOMOUS QUADRATIC CHAOTIC SYSTEM WITH TWO STABLE NODE-FOCI

2010 ◽  
Vol 20 (04) ◽  
pp. 1061-1083 ◽  
Author(s):  
QIGUI YANG ◽  
ZHOUCHAO WEI ◽  
GUANRONG CHEN
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Type Systems ◽  
Homoclinic Orbits ◽  
Stable Node ◽  
Algebraic Form ◽  
Special Cases ◽  
New Chaotic System ◽  
Parameter Values ◽  
New System

This paper reports the finding of an unusual three-dimensional autonomous quadratic Lorenz-like chaotic system which, surprisingly, has two stable node-type of foci as its only equilibria. The new system contains the diffusionless Lorenz system and the Burke–Shaw system, and some others, as special cases. The algebraic form of the new chaotic system is similar to the other Lorenz-type systems, but they are topologically nonequivalent. To further analyze the new system, some dynamical behaviors such as Hopf bifurcation and singularly degenerate heteroclinic and homoclinic orbits, are rigorously proved with simulation verification. Moreover, it is proved that the new system with some specified parameter values has Silnikov-type homoclinic and heteroclinic chaos.

Generating coexisting attractors from a new four-dimensional chaotic system

2020 ◽  
pp. 2150035
Author(s):  
Yan-Mei Hu ◽  
Bang-Cheng Lai
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Linear Functions ◽  
Chaotic Attractors ◽  
Dynamic Evolution ◽  
Coexisting Attractors ◽  
Evolution Analysis ◽  
Fixed Parameter ◽  
Parameter Values ◽  
Multiple Coexisting Attractors

This paper introduces a new four-dimensional chaotic system with a unique unstable equilibrium and multiple coexisting attractors. The dynamic evolution analysis shows that the system concurrently generates two symmetric chaotic attractors for fixed parameter values. Based on this system, an effective method is established to construct an infinite number of coexisting chaotic attractors. It shows that the introduction of some non-linear functions with multiple zeros can increase the equilibria and inspire the generation of coexisting attractor of the system. Numerical simulations verify the availability of the method.

scholarly journals Periodic perturbations of quadratic planar polynomial vector fields

2002 ◽  
Vol 74 (2) ◽  
pp. 193-198 ◽  
Author(s):  
MARCELO MESSIAS
Keyword(s):  
Vector Fields ◽  
Dynamical Behavior ◽  
Saddle Points ◽  
Heteroclinic Cycle ◽  
Polynomial Vector ◽  
Polynomial Vector Fields ◽  
Poincaré Compactification ◽  
Stable And Unstable Manifolds ◽  
Perturbed System ◽  
Periodic Perturbations

In this work are studied periodic perturbations, depending on two parameters, of quadratic planar polynomial vector fields having an infinite heteroclinic cycle, which is an unbounded solution joining two saddle points at infinity. The global study envolving infinity is performed via the Poincaré compactification. The main result obtained states that for certain types of periodic perturbations, the perturbed system has quadratic heteroclinic tangencies and transverse intersections between the local stable and unstable manifolds of the hyperbolic periodic orbits at infinity. It implies, via the Birkhoff-Smale Theorem, in a complex dynamical behavior of the solutions of the perturbed system, in a finite part of the phase plane.

Dynamical analysis, FPGA implementation and synchronization for secure communication of new chaotic system with hidden and coexisting attractors

2021 ◽  
Author(s):  
Qiang Lai ◽  
Ziling Wang ◽  
Paul Didier Kamdem Kuate
Keyword(s):  
Chaotic System ◽  
Secure Communication ◽  
Analog Circuit ◽  
Control Method ◽  
Simulation Analysis ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Dynamical Analysis ◽  
Hidden Attractors ◽  
Coexisting Attractors

This paper proposes an interesting autonomous chaotic system with hidden attractors and coexisting attractors. The system has no equilibrium, one equilibrium, three equilibria and line equilibria for different parameter regions. The existence of hidden attractors and coexisting attractors of the system has been revealed by using simulation analysis. The bifurcation diagram shows the period-doubling bifurcation route to chaos with the variation of parameters. The analog circuit and FPGA implementation of the system are presented. The synchronization for secure communication of the system is investigated. The synchronization conditions are established by using the adaptive control method.

Sign in / Sign up

Export Citation Format

Share Document