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

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.

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.

scholarly journals Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features

Entropy ◽  
2020 ◽  
Vol 23 (1) ◽  
pp. 48
Author(s):  
Hayder Natiq ◽  
Muhammad Rezal Kamel Ariffin ◽  
Muhammad Asyraf Asbullah ◽  
Zahari Mahad ◽  
Mohammed Najah
Keyword(s):  
Power Input ◽  
Sample Entropy ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Stable Model ◽  
Analysis Framework ◽  
Plasma Model ◽  
Pseudorandom Sequences ◽  
Periodic Attractors ◽  
Pellet Injection

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.

scholarly journals Analysis and electronic circuit implementation of an integer-and fractional-order Shimizu-Morioka system

2021 ◽  
Vol 67 (6 Nov-Dec) ◽  
Author(s):  
François Kapche Tagne ◽  
Guillaume Honoré KOM ◽  
Marceline Motchongom Tingue ◽  
Pierre Kisito Talla ◽  
V. Kamdoum Tamba
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Close Agreement ◽  
Electronic Circuit ◽  
Dynamical Behavior ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Circuit Implementation ◽  
Bifurcation Structures ◽  
Electronic Circuit Implementation

The dynamics of an integer-order and fractional-order Lorenz like system called Shimizu-Morioka system is investigated in this paper. It is shown thatinteger-order Shimizu-Morioka system displays bistable chaotic attractors, monostable chaotic attractors and coexistence between bistable and monostable chaotic attractors. For suitable choose of parameters, the fractional-order Shimizu-Morioka system exhibits bistable chaotic attractors, monostable chaotic attractors, metastable chaos (i.e. transient chaos) and spiking oscillations. The bifurcation structures reveal that the fractional-order derivative affects considerably the dynamics of Shimizu-Morioka system. The chain fractance circuit is used to designand implement the integer- and fractional-order Shimizu-Morioka system in Pspice. A close agreement is observed between PSpice based circuit simulations and numerical simulations analysis. The results obtained in this work were not reported previously in the interger as well as in fractional-order Shimizu-Morioka system and thus represent an important contribution which may help us in better understanding of the dynamical behavior of this class of systems.

ON THE BIFURCATION PHENOMENA OF THE KURAMOTO–SIVASHINSKY EQUATION

1993 ◽  
Vol 03 (05) ◽  
pp. 1299-1303 ◽  
Author(s):  
FRED FEUDEL ◽  
ULRIKE FEUDEL ◽  
AXEL BRANDENBURG
Keyword(s):  
Periodic Solution ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Transient Chaos ◽  
Bifurcation Parameter ◽  
Periodic Motions ◽  
Chaotic Region ◽  
Bifurcation Phenomena ◽  
Route To Chaos ◽  
Sivashinsky Equation

Bifurcation phenomena of the Kuramoto–Sivashinsky equation have been studied numerically. The solutions considered are restricted to the invariant subspace of odd functions. One possible route to chaos via a period-doubling cascade is investigated in detail: The four-modal steady-state loses its stability through a Hopf bifurcation and a branch of periodic motions is created. After a symmetry breaking the periodic solution undergoes a period-doubling cascade which ends up in two antisymmetric chaotic attractors. A merging of these antisymmetric attractors to a symmetric one is observed. The chaotic branch depending on the bifurcation parameter is characterized by the values of the Lyapunov exponents. Periodic windows within the chaotic region are also detected. Finally, a further increase of the bifurcation parameter leads to a transition from the attractor into transient chaos.

Visualization analysis on stretch-and-fold mechanism of chaotic attractors

2014 ◽  
Vol 1 ◽  
pp. 443-446
Author(s):  
Yutaka Shimada ◽  
Takuya Kobayashi ◽  
Tohru Ikeguchi ◽  
Kazuyuki Aihara
Keyword(s):  
Chaotic Attractors ◽  
Visualization Analysis

A MODIFIED GENERALIZED LORENZ-TYPE SYSTEM AND ITS CANONICAL FORM

2009 ◽  
Vol 19 (06) ◽  
pp. 1931-1949 ◽  
Author(s):  
QIGUI YANG ◽  
KANGMING ZHANG ◽  
GUANRONG CHEN
Keyword(s):  
Special Form ◽  
Topological Structure ◽  
Complex Dynamics ◽  
Type System ◽  
Chaotic Attractors ◽  
Hopf Bifurcations ◽  
Compound Structure ◽  
Two Parameters ◽  
First Time ◽  
New System

In this paper, a modified generalized Lorenz-type system is introduced, which is state-equivalent to a simple and special form, and is parameterized by two parameters useful for chaos turning and system classification. More importantly, based on the parameterized form, two classes of new chaotic attractors are found for the first time in the literature, which are similar but nonequivalent in topological structure. To further understand the complex dynamics of the new system, some basic properties such as Lyapunov exponents, Hopf bifurcations and compound structure of the attractors are analyzed and demonstrated with careful numerical simulations.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

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