scholarly journals A New Chaotic System with Only Nonhyperbolic Equilibrium Points: Dynamics and Its Engineering Application

Complexity ◽  
2022 ◽  
Vol 2022 ◽  
pp. 1-16
Author(s):  
Maryam Zolfaghari-Nejad ◽  
Mostafa Charmi ◽  
Hossein Hassanpoor
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Equilibrium Points ◽  
Engineering Application ◽  
Period Doubling ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
Initial Values ◽  
New Chaotic System ◽  
New System

In this work, we introduce a new non-Shilnikov chaotic system with an infinite number of nonhyperbolic equilibrium points. The proposed system does not have any linear term, and it is worth noting that the new system has one equilibrium point with triple zero eigenvalues at the origin. Also, the novel system has an infinite number of equilibrium points with double zero eigenvalues that are located on the z -axis. Numerical analysis of the system reveals many strong dynamics. The new system exhibits multistability and antimonotonicity. Multistability implies the coexistence of many periodic, limit cycle, and chaotic attractors under different initial values. Also, bifurcation analysis of the system shows interesting phenomena such as periodic window, period-doubling route to chaos, and inverse period-doubling bifurcations. Moreover, the complexity of the system is analyzed by computing spectral entropy. The spectral entropy distribution under different initial values is very scattered and shows that the new system has numerous multiple attractors. Finally, chaos-based encoding/decoding algorithms for secure data transmission are developed by designing a state chain diagram, which indicates the applicability of the new chaotic system.

A Novel No-Equilibrium Chaotic System with Multiwing Butterfly Attractors

2015 ◽  
Vol 25 (04) ◽  
pp. 1550056 ◽  
Author(s):  
Fadhil Rahma Tahir ◽  
Sajad Jafari ◽  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
State Feedback ◽  
Equilibrium Points ◽  
Research Topic ◽  
Feedback Controller ◽  
Strange Attractors ◽  
State Feedback Controller ◽  
New Chaotic System ◽  
New System

Discovering unknown features of no-equilibrium systems with hidden strange attractors is an attractive research topic. This paper presents a novel no-equilibrium chaotic system that is constructed by using a state feedback controller. Interestingly, the new system can exhibit multiwing butterfly attractors. Moreover, a new chaotic system with an infinite number of equilibrium points, which can generate multiscroll attractors, is also proposed by applying the introduced methodology.

Different Families of Hidden Attractors in a New Chaotic System with Variable Equilibrium

2017 ◽  
Vol 27 (09) ◽  
pp. 1750138 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
Christos Volos ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
View Point ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Complex Dynamical Behavior ◽  
New System

A new chaotic system having variable equilibrium is introduced in this paper. The presence of an infinite number of equilibrium points, a stable equilibrium, and no-equilibrium is observed in the system. Interestingly, this system is classified as a rare system with hidden attractors from the view point of computation. Complex dynamical behavior and a circuital implementation of the new system have been investigated in our work.

scholarly journals A New Four-Scroll Chaotic System with a Self-Excited Attractor and Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1931 ◽  
Author(s):  
Sivaperumal Sampath ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Mustafa Mamat ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Model ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new four-scroll chaotic system with four nonlinearities. The proposed system is a new addition to existing multi-scroll chaotic systems in the literature. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. As the new four-scroll chaotic system is shown to have three unstable equilibrium points, it has a self-excited chaotic attractor. An electronic circuit simulation of the new four-scroll chaotic system is shown using MultiSIM to check the feasibility of the four-scroll chaotic model.

A Novel Class of Chaotic Flows with Infinite Equilibriums and Their Application in Chaos-Based Communication Design Using DCSK

2018 ◽  
Vol 73 (7) ◽  
pp. 609-617 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Serdar Çiçek ◽  
Abdul Jalil M. Khalaf ◽  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
...  
Keyword(s):  
Chaotic System ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Engineering Application ◽  
Chaotic Flows ◽  
Fundamental Properties ◽  
New Chaotic System ◽  
Shift Keying ◽  
Chaos Shift Keying

AbstractDiscovering chaotic systems with interesting features has been of interest in the recent years. One such important and interesting feature is the type and shape of equilibrium points. We introduce a class of chaotic systems which could show different types of infinite equilibrium points. The fundamental properties of the proposed systems like bifurcation diagram and Lyapunov exponents are investigated. An electronic circuit of the presented chaotic systems is implemented. In addition, a chaos-based communication application by the differential chaos shift keying method with the new chaotic system is designed and tested for engineering application. According to the design test results, the proposed chaos-based communication system is successful. Therefore, the new chaotic system can be used in chaos-based communication systems.

scholarly journals A Chaotic System with an Infinite Number of Equilibrium Points: Dynamics, Horseshoe, and Synchronization

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Christos Volos ◽  
Sundarapandian Vaidyanathan ◽  
Xiong Wang
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Systems ◽  
Chaotic Behavior ◽  
Equilibrium Points ◽  
Equilibrium Analysis ◽  
Chaotic Attractors ◽  
Hidden Attractors ◽  
New Chaotic System ◽  
Topological Horseshoes

Discovering systems with hidden attractors is a challenging topic which has received considerable interest of the scientific community recently. This work introduces a new chaotic system having hidden chaotic attractors with an infinite number of equilibrium points. We have studied dynamical properties of such special system via equilibrium analysis, bifurcation diagram, and maximal Lyapunov exponents. In order to confirm the system’s chaotic behavior, the findings of topological horseshoes for the system are presented. In addition, the possibility of synchronization of two new chaotic systems with infinite equilibria is investigated by using adaptive control.

scholarly journals Abundant Coexisting Multiple Attractors’ Behaviors in Three-Dimensional Sine Chaotic System

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Huagan Wu ◽  
Han Bao ◽  
Quan Xu ◽  
Mo Chen
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Three Dimensional ◽  
Multiple Attractors ◽  
One Dimensional ◽  
System Parameters ◽  
Initial Values ◽  
Power Simulation ◽  
Attraction Basins ◽  
Index 2

This paper presents a novel and simple three-dimensional (3-D) chaotic system by introducing two sine nonlinearities into a simple 3-D linear dynamical system. The presented sine system possesses nine equilibrium points consisting of five index-2 saddle foci and four index-1 saddle foci which allow the coexistence of various types of disconnected attractors, also known as multistability. The coexisting multiple attractors are depicted by the phase plots and attraction basins. Coexisting bifurcation modes triggered by different initial values are numerically simulated by two-dimensional bifurcation and complexity plots under two sets of initial values and one-dimensional bifurcation plots under three sets of initial values, which demonstrate that the abundant coexisting multiple attractors’ behaviors in the presented sine system are related not only to the system parameters but also to the initial values. A simulation-oriented circuit model is synthesized, and PSIM (power simulation) screen captures well validate the numerical simulations.

scholarly journals A New Chaotic System with a Pear-shaped Equilibrium and its Circuit Simulation

2018 ◽  
Vol 8 (6) ◽  
pp. 4951 ◽  
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Mustafa Mamat ◽  
Muhammad Afendee Mohamed ◽  
Mada Sanjaya WS
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Equilibrium Curve ◽  
New Chaotic System ◽  
Electronic Circuit Simulation ◽  
New System

This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility.

Constructing a Chaotic System with an Infinite Number of Equilibrium Points

2016 ◽  
Vol 26 (13) ◽  
pp. 1650225 ◽  
Author(s):  
Viet-Thanh Pham ◽  
Sajad Jafari ◽  
Tomasz Kapitaniak
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Chaotic Systems ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Hidden Attractors ◽  
Memristive Device ◽  
New System

The chaotic systems with hidden attractors, such as chaotic systems with a stable equilibrium, chaotic systems with infinite equilibria or chaotic systems with no equilibrium have been investigated recently. However, the relationships between them still need to be discovered. This work explains how to transform a system with one stable equilibrium into a new system with an infinite number of equilibrium points by using a memristive device. Furthermore, some other new systems with infinite equilibria are also constructed to illustrate the introduced methodology.

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 A Hidden Chaotic System with Multiple Attractors

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1341
Author(s):  
Xiefu Zhang ◽  
Zean Tian ◽  
Jian Li ◽  
Xianming Wu ◽  
Zhongwei Cui
Keyword(s):  
Phase Diagram ◽  
Lyapunov Exponent ◽  
Numerical Methods ◽  
Chaotic System ◽  
Time Domain ◽  
Chaotic Attractor ◽  
Largest Lyapunov Exponent ◽  
Spectral Entropy ◽  
Multiple Attractors ◽  
System Parameters

This paper reports a hidden chaotic system without equilibrium point. The proposed system is studied by the software of MATLAB R2018 through several numerical methods, including Largest Lyapunov exponent, bifurcation diagram, phase diagram, Poincaré map, time-domain waveform, attractive basin and Spectral Entropy. Seven types of attractors are found through altering the system parameters and some interesting characteristics such as coexistence attractors, controllability of chaotic attractor, hyperchaotic behavior and transition behavior are observed. Particularly, the Spectral Entropy algorithm is used to analyze the system and based on the normalized values of Spectral Entropy, the state of the studied system can be identified. Furthermore, the system has been implemented physically to verify the realizability.

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