A Modified Multistable Chaotic Oscillator

2018 ◽  
Vol 28 (07) ◽  
pp. 1850085 ◽  
Author(s):  
Zhouchao Wei ◽  
Viet-Thanh Pham ◽  
Abdul Jalil M. Khalaf ◽  
Jacques Kengne ◽  
Sajad Jafari
Keyword(s):  
Chaotic System ◽  
Limit Cycles ◽  
Initial Conditions ◽  
Chaotic Oscillator ◽  
Two Dimensional ◽  
Different Types ◽  
New System

In this paper, by modifying a known two-dimensional oscillator, we obtain an interesting new oscillator with coexisting limit cycles and point attractors. Then by changing this new system to its forced version and choosing a proper set of parameters, we introduce a chaotic system with some very interesting features. In this system, not only can we see the coexistence of different types of attractors, but also a fascinating phenomenon: some initial conditions can escape from the gravity of nearby attractors and travel far away before being trapped in an attractor beyond the usual access.

A Compact and Low Power Realization of a High Frequency Chaotic Oscillator

2017 ◽  
Vol 2017 (DPC) ◽  
pp. 1-27
Author(s):  
R. Chase Harrison ◽  
Benjamin K. Rhea ◽  
Frank T. Werner ◽  
Robert N. Dean
Keyword(s):  
Low Power ◽  
Chaotic System ◽  
High Frequency ◽  
High Speed ◽  
Random Number ◽  
Nonlinear Dynamical Systems ◽  
Initial Conditions ◽  
Random Number Generation ◽  
Chaotic Oscillator ◽  
Number Generation

The desirable properties exhibited in some nonlinear dynamical systems have many potential uses. These properties include sensitivity to initial conditions, wide bandwidth, and long-term aperiodicity, which lend themselves to applications such as random number generation, communication and audio ranging systems. Chaotic systems can be realized in electronics by using inexpensive and readily available parts. Many of these systems have been verified in electronics using nonpermanent prototyping at very low frequencies; however, this restricts the range of potential applications. In particular, random number generation (RNG) benefits from an increase in operation frequency, since it is proportional to the amount of bits that can be produced per second. This work looks specifically at the nonlinear element in the chaotic system and evaluates its frequency limitations in electronics. In practice, many of nonlinearities are difficult to implement in high speed electronics. In addition to this restriction, the use of complex feedback paths and large inductors prevents the miniaturization that is desirable for implementing chaotic circuits in other electronic systems. By carefully analyzing the fundamental dynamics that govern the chaotic system, these problems can be addressed. Presented in this work is the design and realization of a high frequency chaotic oscillator that exhibits complex and rich dynamics while using a compact footprint and low power consumption.

scholarly journals Composite One- to Six-Scroll Hidden Attractors in a Memristor-Based Chaotic System and Their Circuit Implementation

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Ying Li ◽  
Xiaozhu Xia ◽  
Yicheng Zeng ◽  
Qinghui Hong
Keyword(s):  
Fixed Point ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Circuit Implementation ◽  
Hidden Attractors ◽  
Coexisting Attractors ◽  
Extreme Multistability ◽  
Different Types ◽  
Hardware Circuit ◽  
New System

Chaotic systems with hidden multiscroll attractors have received much attention in recent years. However, most parts of hidden multiscroll attractors previously reported were repeated by the same type of attractor, and the composite of different types of attractors appeared rarely. In this paper, a memristor-based chaotic system, which can generate composite attractors with one up to six scrolls, is proposed. These composite attractors have different forms, similar to the Chua’s double scroll and jerk double scroll. Through theoretical analysis, we find that the new system has no fixed point; that is to say, all of the composite multiscroll attractors are hidden attractors. Additionally, some complicated dynamic behaviors including various hidden coexisting attractors, extreme multistability, and transient transition are explored. Moreover, hardware circuit using discrete components is implemented, and its experimental results supported the numerical simulations results.

Design of a New 3D Chaotic System Producing Infinitely Many Coexisting Attractors and Its Application to Weak Signal Detection

2021 ◽  
Vol 31 (15) ◽  
Author(s):  
Bing Liu ◽  
Xiaolin Ye ◽  
Gang Hu
Keyword(s):  
Signal Detection ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Initial Conditions ◽  
Control Function ◽  
Detection System ◽  
Chaotic Oscillator ◽  
Weak Signal ◽  
Weak Signal Detection ◽  
Coexisting Attractors

This paper proposes a new 3D chaotic system, which can produce infinitely many coexisting attractors. By introducing a boosted control of cosine function to an original chaotic system, as the initial conditions periodically change, the proposed chaotic system can spontaneously output infinitely many chaotic sequences of different amplitudes in two directions in the phase plane. This means that the proposed system can output more key information as a pseudo-random signal generator (PRSG). This is of great significance in the research of weak signal detection. In comparison with the original chaotic system, the chaotic behavior of the proposed system is obviously enhanced due to the introduction of the boosted control function. Then, by adding the mathematical models of a weak signal and a noise signal to the proposed chaotic system, a new chaotic oscillator, which is sensitive to the weak signal, can be restructured. With the change of weak signal amplitude and angular frequency, the dynamical state of the detection system will generate a big difference, which indicates that the weak signal can be detected successfully. Finally, the proposed chaotic system model is physically realized by DSP (Digital Signal Processing), which shows its feasibility in industrial implementation. Especially, since a third-order chaotic system is the lowest-dimensional continuous system that can generate infinitely many coexisting attractors, the proposed chaotic system is of great value in the basic research of chaos.

A New Megastable Oscillator with Rational and Irrational Parameters

2019 ◽  
Vol 29 (13) ◽  
pp. 1950176 ◽  
Author(s):  
Zhen Wang ◽  
Ibrahim Ismael Hamarash ◽  
Payam Sadeghi Shabestari ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Infinite Number ◽  
Limit Cycles ◽  
Nonlinear Oscillator ◽  
Analog Circuit ◽  
Strange Attractors ◽  
Two Dimensional ◽  
System A ◽  
New System

In this paper, a new two-dimensional nonlinear oscillator with an unusual sequence of rational and irrational parameters is introduced. This oscillator has endless coexisting limit cycles, which make it a megastable dynamical system. By periodically forcing this system, a new system is designed which is capable of exhibiting an infinite number of coexisting asymmetric torus and strange attractors. This system is implemented by an analog circuit, and its Hamiltonian energy is calculated.

scholarly journals A High Spectral Entropy (SE) Memristive Hidden Chaotic System with Multi-Type Quasi-Periodic and its Circuit

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 1026 ◽  
Author(s):  
Licai Liu ◽  
Chuanhong Du ◽  
Lixiu Liang ◽  
Xiefu Zhang
Keyword(s):  
Chaotic System ◽  
Limit Cycles ◽  
Initial Conditions ◽  
Chaotic Attractors ◽  
Spectral Entropy ◽  
High Complexity ◽  
Hidden Attractors ◽  
Nonlinear Characteristics ◽  
System Use ◽  
New Type

As a new type of nonlinear electronic component, a memristor can be used in a chaotic system to increase the complexity of the system. In this paper, a flux-controlled memristor is applied to an existing chaotic system, and a novel five-dimensional chaotic system with high complexity and hidden attractors is proposed. Analyzing the nonlinear characteristics of the system, we can find that the system has new chaotic attractors and many novel quasi-periodic limit cycles; the unique attractor structure of the Poincaré map also reflects the complexity and novelty of the hidden attractor for the system; the system has a very high complexity when measured through spectral entropy. In addition, under different initial conditions, the system exhibits the coexistence of chaotic attractors with different topologies, quasi-periodic limit cycles, and chaotic attractors. At the same time, an interesting transient chaos phenomenon, one kind of novel quasi-periodic, and weak chaotic hidden attractors are found. Finally, we realize the memristor model circuit and the proposed chaotic system use off-the-shelf electronic components. The experimental results of the circuit are consistent with the numerical simulation, which shows that the system is physically achievable and provides a new option for the application of memristive chaotic systems.

scholarly journals Design and Analysis of a Novel Six-Dimensional Hyper Chaotic System

2020 ◽  
Vol 31 (4) ◽  
pp. 62
Author(s):  
Sadiq A. Mehdi ◽  
Shatha Jassim Muhamed
Keyword(s):  
Lyapunov Exponents ◽  
Chaotic System ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Waveform Analysis ◽  
Phase Portraits ◽  
Qualitative Properties ◽  
New Chaotic System ◽  
Basic Characteristics ◽  
New System

The chaotic system has been widely studied. A new six-dimension hyper chaotic system is introduced in this paper. We used a new chaotic system based on a six-dimension for the purpose of increasing chaos in the system, where the new system has eleven positive parameters, complicated chaotic dynamics behaviors and gives an analysis of the new systems. The basic characteristics and dynamic behavior of this system are investigated with a presence of chaotic attractor, Dissipativity, symmetry, equilibrium points, Lyapunov Exponents, Kaplan-Yorke dimension, waveform analysis and sensitivity toward initial conditions. The results of the analysis exhibit that the new system contains three unstable equilibrium points and the six Lyapunov exponents. Maxim non-negative Lyapunov Exponent (MLE) is obtained as 4.72625, and Kaplan-Yorke are obtained as 3.92566, and the new system characteristics with, unstable, high complexity, and unpredictability, the new system dynamics is simulated utilizing MATHEMATICA program. The phase portraits and the qualitative properties of the new hyper chaotic system have been described at the detail.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

scholarly journals Composite hollow truss with multiple vierendeel panels

2013 ◽  
Vol 66 (4) ◽  
pp. 431-438
Author(s):  
Augusto Ottoni Bueno da Silva ◽  
Newton de Oliveira Pinto Júnior ◽  
João Alberto Venegas Requena
Keyword(s):  
Bearing Capacity ◽  
Failure Modes ◽  
Three Dimensional ◽  
Analytical Calculation ◽  
Two Dimensional ◽  
Shear Forces ◽  
Vertical Displacements ◽  
New System ◽  
The Ideal

The aim of this study was to evaluate through analytical calculation, two-dimensional elastic modeling, and three-dimensional plastic modeling, the bearing capacity and failure modes of composite hollow trusses bi-supported with a 15 meter span, varying the number of central Vierendeel panels. The study found the proportion span/3 - span/3 - span/3, as the ideal relationship for the truss - Vierendeel - truss lengths, because by increasing the proportion of the length occupied by the central Vierendeel panels, the new system loses stiffness and no longer supports the load stipulated in the project. Furthermore, they can start presenting excessive vertical displacements and insufficient resistance to external shear forces acting on the panels.

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