Analysis of a new 3D smooth autonomous system with different wing chaotic attractors and transient chaos

2010 ◽  
Vol 62 (1-2) ◽  
pp. 391-405 ◽  
Author(s):  
Sara Dadras ◽  
Hamid Reza Momeni ◽  
Guoyuan Qi
Keyword(s):  
Autonomous System ◽  
Chaotic Attractors ◽  
Transient Chaos

A 3D Autonomous System with Infinitely Many Chaotic Attractors

2019 ◽  
Vol 29 (12) ◽  
pp. 1950166 ◽  
Author(s):  
Ting Yang ◽  
Qigui Yang
Keyword(s):  
Dynamical System ◽  
Differential Equations ◽  
Autonomous System ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Double Zero ◽  
Finite Dimensional ◽  
Periodic Attractors ◽  
The Stability ◽  
Autonomous Dynamical System

Intuitively, a finite-dimensional autonomous system of ordinary differential equations can only generate finitely many chaotic attractors. Amazingly, however, this paper finds a three-dimensional autonomous dynamical system that can generate infinitely many chaotic attractors. Specifically, this system can generate infinitely many coexisting chaotic attractors and infinitely many coexisting periodic attractors in the following three cases: (i) no equilibria, (ii) only infinitely many nonhyperbolic double-zero equilibria, and (iii) both infinitely many hyperbolic saddles and nonhyperbolic pure-imaginary equilibria. By analyzing the stability of double-zero and pure-imaginary equilibria, it is shown that the classic Shil’nikov criteria fail in verifying the existence of chaos in the above three cases.

scholarly journals Complex Dynamics of a Novel Chaotic System Based on an Active Memristor

Electronics ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 410 ◽  
Author(s):  
Qinghai Song ◽  
Hui Chang ◽  
Yuxia Li
Keyword(s):  
Signal Processing ◽  
Complex Dynamics ◽  
Digital Signal ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
State Switching ◽  
Autonomous Differential Equations

On the basis of the bistable bi-local active memristor (BBAM), an active memristor (AM) and its emulator were designed, and the characteristic fingerprints of the memristor were found under the applied periodic voltage. A memristor-based chaotic circuit was constructed, whose corresponding dynamics system was described by the 4-D autonomous differential equations. Complex dynamics behaviors, including chaos, transient chaos, heterogeneous coexisting attractors, and state-switches of the system were analyzed and explored by using Lyapunov exponents, bifurcation diagrams, phase diagrams, and Poincaré mapping, among others. In particular, a novel exotic chaotic attractor of the system was observed, as well as the singular state-switching between point attractors and chaotic attractors. The results of the theoretical analysis were verified by both circuit experiments and digital signal processing (DSP) technology.

Constructing a Chaotic System with Any Number of Attractors

2017 ◽  
Vol 27 (08) ◽  
pp. 1750118 ◽  
Author(s):  
Xu Zhang
Keyword(s):  
Vector Field ◽  
Geometric Structure ◽  
Autonomous System ◽  
Dynamical Behavior ◽  
Basin Of Attraction ◽  
Original System ◽  
Chaotic Attractors ◽  
Global Dynamics ◽  
The Basin Of Attraction ◽  
New System

Applying some transformation to an autonomous system, we obtain a new system, which might keep the dynamical behavior of the original system or generate different dynamics. But this is often accompanied by the appearance of discontinuous points, where the vector field for the new system is not continuous at these points. We discuss the effects of the discontinuous points, and provide two methods to construct systems with any preassigned number of chaotic attractors via some transformation. The first one does not change the geometric structure of the attractors, since the discontinuous points are out of the basin of attraction. The second one might make the new systems have different dynamics, like multiscroll chaotic attractors, or infinitely many chaotic attractors. These results illustrate that both the equilibria and the discontinuous points affect the global dynamics.

Crises, sudden changes in chaotic attractors, and transient chaos

1983 ◽  
Vol 7 (1-3) ◽  
pp. 181-200 ◽  
Author(s):  
Celso Grebogi ◽  
Edward Ott ◽  
James A. Yorke
Keyword(s):  
Chaotic Attractors ◽  
Transient Chaos

ENCODING DIGITAL INFORMATION USING TRANSIENT CHAOS

2000 ◽  
Vol 10 (04) ◽  
pp. 787-795 ◽  
Author(s):  
YING-CHENG LAI
Keyword(s):  
Nonlinear Systems ◽  
Information Source ◽  
Channel Noise ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Digital Information ◽  
Symbolic Representations ◽  
Chaotic Orbits ◽  
Control Scheme ◽  
Digital Encoding

Recent work has demonstrated that symbolic representations of controlled chaotic orbits can be utilized for encoding digital information. So far, this idea has been demonstrated using systems exhibiting sustained chaotic motion on chaotic attractors. The purpose of this work is to explore digital encoding by using transient chaos naturally arising in nonlinear systems. Dynamically, transient chaos is caused by nonattracting chaotic saddles. We argue that there are two major advantages when trajectories on chaotic saddles are exploited as information source: (1) the channel capacity can in general be large, and (2) the influence of channel noise can be reduced. We present a control scheme and also a practical example of encoding a digital message.

Multistability in a 3D Autonomous System with Different Types of Chaotic Attractors

2021 ◽  
Vol 31 (02) ◽  
pp. 2150028
Author(s):  
Ting Yang
Keyword(s):  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Autonomous System ◽  
Heteroclinic Orbits ◽  
Chaotic Attractors ◽  
Different Types ◽  
Lyapunov Coefficient ◽  
Weak Saddle

This paper investigates multistability in a 3D autonomous system with different types of chaotic attractors, which are not in the sense of Shil’nikov criteria. First, under some conditions, the system has infinitely many isolated equilibria. Moreover, all equilibria are nonhyperbolic and give the first Lyapunov coefficient. Furthermore, when all equilibria are weak saddle-foci, the system also has infinitely many chaotic attractors. Besides, the Lyapunov exponents spectrum and bifurcation diagram are given. Second, under another condition, all the equilibria constitute a curve and there exist infinitely many singular degenerated heteroclinic orbits. At the same time, the system can show infinitely many chaotic attractors.

A Novel Cubic–Equilibrium Chaotic System with Coexisting Hidden Attractors: Analysis, and Circuit Implementation

2017 ◽  
Vol 27 (04) ◽  
pp. 1850066 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
Autonomous System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Complex Dynamics ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Dynamical Properties

Chaotic systems with a curve of equilibria have attracted considerable interest in theoretical researches and engineering applications because they are categorized as systems with hidden attractors. In this paper, we introduce a new three-dimensional autonomous system with cubic equilibrium. Fundamental dynamical properties and complex dynamics of the system have been investigated. Of particular interest is the coexistence of chaotic attractors in the proposed system. Furthermore, we have designed and implemented an electronic circuit to verify the feasibility of such a system with cubic equilibrium.

BIFURCATION AND CHAOS IN COUPLED BVP OSCILLATORS

2004 ◽  
Vol 14 (04) ◽  
pp. 1305-1324 ◽  
Author(s):  
TETSUSHI UETA ◽  
HISAYO MIYAZAKI ◽  
TAKUJI KOUSAKA ◽  
HIROSHI KAWAKAMI
Keyword(s):  
Autonomous System ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Nonlinear Phenomena ◽  
Van Der Pol ◽  
Bifurcation And Chaos ◽  
Experimental Laboratory ◽  
Chaotic Parameter ◽  
Parameter Values ◽  
The Mathematical Model

Bonhöffer–van der Pol(BVP) oscillator is a classic model exhibiting typical nonlinear phenomena in the planar autonomous system. This paper gives an analysis of equilibria, periodic solutions, strange attractors of two BVP oscillators coupled by a resister. When an oscillator is fixed its parameter values in nonoscillatory region and the others in oscillatory region, create the double scroll attractor due to the coupling. Bifurcation diagrams are obtained numerically from the mathematical model and chaotic parameter regions are clarified. We also confirm the existence of period-doubling cascades and chaotic attractors in the experimental laboratory.

Sign in / Sign up

Export Citation Format

Share Document