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 A Simple Parallel Chaotic Circuit Based on Memristor

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 719
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Zhongwei Cui
Keyword(s):  
Time Domain ◽  
Sample Entropy ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Chaotic Circuit ◽  
Coexisting Attractors ◽  
Periodic Attractors ◽  
Dynamic Map ◽  
Lyapunov Exponent Spectrum

This paper reports a simple parallel chaotic circuit with only four circuit elements: a capacitor, an inductor, a thermistor, and a linear negative resistor. The proposed system was analyzed with MATLAB R2018 through some numerical methods, such as largest Lyapunov exponent spectrum (LLE), phase diagram, Poincaré map, dynamic map, and time-domain waveform. The results revealed 11 kinds of chaotic attractors, 4 kinds of periodic attractors, and some attractive characteristics (such as coexistence attractors and transient transition behaviors). In addition, spectral entropy and sample entropy are adopted to analyze the phenomenon of coexisting attractors. The theoretical analysis and numerical simulation demonstrate that the system has rich dynamic characteristics.

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.

LOGISTIC MAPPING WITH A TIME-DEPENDENT SYSTEM-PARAMETER AND ITS ATTRACTOR BASINS WITH SELF-SIMILAR STRUCTURE

2004 ◽  
Vol 14 (07) ◽  
pp. 2407-2416 ◽  
Author(s):  
JOUSUKE KUROIWA ◽  
TAKAFUMI MIKI
Keyword(s):  
System Parameter ◽  
Time Dependent ◽  
Chaotic Attractors ◽  
Self Similarity ◽  
Initial Values ◽  
Logistic Mapping ◽  
Periodic Attractors ◽  
Self Similar ◽  
Basins Of Attractions ◽  
Time Dependent System

In this paper, logistic mapping with a time-dependent system-parameter (referred as "LMTD") is proposed. In various choices of time dependence, the periodic one has been tried in order to investigate the dynamical properties of LMTD. In certain parameter regions, two different attractors coexist depending on the initial values, for instances, two different chaotic attractors, two different periodic attractors, or two periodic/chaotic attractors. In addition, the whole configuration space of the initial values forms basins of attractions of which structures indicate self-similarity.

scholarly journals Dynamics of a Heterogeneous Constraint Profit Maximization Duopoly Model Based on an Isoelastic Demand

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
S. S. Askar ◽  
A. Ibrahim ◽  
A. A. Elsadany
Keyword(s):  
Basin Of Attraction ◽  
Profit Maximization ◽  
Period Doubling ◽  
Chaotic Attractors ◽  
Cournot Duopoly ◽  
Coexistence Of Attractors ◽  
Duopoly Model ◽  
Periodic Attractors ◽  
Initial Results ◽  
The Basin Of Attraction

A Cournot duopoly game is a two-firm market where the aim is to maximize profits. It is rational for every company to maximize its profits with minimal sales constraints. As a consequence, a model of constrained profit maximization (CPM) occurs when a business needs to be increased with profit minimal sales constraints. The CPM model, in which companies maximize profits under the minimum sales constraints, is an alternative to the profit maximization model. The current study constructs a duopoly game based on an isoelastic demand and homogeneous goods with heterogeneous strategies. In the event of sales constraint and no sales constraint, the local stability conditions of the Cournot equilibrium are derived. The initial results show that the duopoly model would be easier to stabilize if firms were to impose certain minimum sales constraints. Two routes to chaos are analyzed by numerical simulation using 2D bifurcation diagram, one of which is period doubling bifurcation and the other is Neimark–Sacker bifurcation. Four forms of coexistence of attractors are demonstrated by the basin of attraction, which is the coexistence of periodic attractors and chaotic attractors, the coexistence of periodic attractors and quasiperiodic attractors, and the coexistence of several chaotic attractors. Our findings show that the effect of game parameters on stability depends on the rules of expectations and restriction of sales by firms.

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

COMPUTATIONAL UNFOLDING OF DOUBLE-CUSP MODELS OF OPINION FORMATION

1991 ◽  
Vol 01 (02) ◽  
pp. 417-430 ◽  
Author(s):  
RALPH ABRAHAM ◽  
ALEXANDER KEITH ◽  
MATTHEW KOEBBE ◽  
GOTTFRIED MAYER-KRESS
Keyword(s):  
Computational Study ◽  
Opinion Dynamics ◽  
Chaotic Attractors ◽  
Cusp Catastrophe ◽  
Opinion Formation ◽  
Catastrophe Model ◽  
Model Study ◽  
Periodic Attractors ◽  
Potential Applications ◽  
Democratic Nation

In 1975, Isnard and Zeeman proposed a cusp catastrophe model for the polarization of a social group, such as the population of a democratic nation. Ten years later, Kadyrov combined two of these cusps into a model for the opinion dynamics of two "nonsocialist" nations. This is a nongradient dynamical system, more general than the double-cusp catastrophe studied by Callahan and Sashin [1987]. Here, we present a computational study of the nongradient double cusp, in which the degeneracy of Kadyrov's model is unfolded in codimension eight. Also, we develop a discrete-time cusp model, study the corresponding double cusp, establish its equivalence to the continuous-time double cusp, and discuss some potential applications. We find bifurcations for multiple critical-point attractors, periodic attractors, and (for the discrete case) bifurcations to quasiperiodic and chaotic attractors.

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 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.

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