scholarly journals A Novel 2D – Grid of Scroll Chaotic Attractor Generated by CNN

Symmetry ◽  
2019 ◽  
Vol 11 (1) ◽  
pp. 99 ◽  
Author(s):  
Ahmed M. Ali ◽  
Saif M. Ramadhan ◽  
Fadhil R. Tahir
Keyword(s):  
Theoretical Analysis ◽  
Chaotic Attractor ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Electronic Circuits ◽  
Nonlinear Networks ◽  
Design And Implementation ◽  
Simulation Results ◽  
New System

The complex grid of scroll chaotic attractors that are generated through nonlinear electronic circuits have been raised considerably over the last decades. In this paper, it is shown that a subclass of Cellular Nonlinear Networks (CNNs) allows us to generate complex dynamics and chaos in symmetry pattern. A novel grid of scroll chaotic attractor, based on a new system, shows symmetry scrolls about the origin. Also, the equilibrium points are located in a manner such that the symmetry about the line x=y has been achieved. The complex dynamics of system can be generated using CNNs, which in turn are derived from a CNN array (1×3) cells. The paper concerns on the design and implementation of 2×2 and 3×3 2D-grid of scroll via the CNN model. Theoretical analysis and numerical simulations of the derived model are included. The simulation results reveal that the grid of scroll attractors can be successfully reproduced using PSpice.

scholarly journals A Meminductor-based Chaotic System

2020 ◽  
Vol 49 (2) ◽  
pp. 317-332
Author(s):  
Aixue Qi ◽  
Lei Ding ◽  
Wenbo Liu
Keyword(s):  
Theoretical Analysis ◽  
Chaotic System ◽  
Phase Trajectory ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Circuit Parameter ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Simulation Results

We propose a meminductor-based chaotic system. Theoretical analysis and numerical simulations reveal complex dynamical behaviors of the proposed meminductor-based chaotic system with five unstable equilibrium points and three different states of chaotic attractors in its phase trajectory with only a single change in circuit parameter. Lyapunov exponents, bifurcation diagrams, and phase portraits are used to investigate its complex chaotic and multi-stability behaviors, including its coexisting chaotic, periodic and point attractors. The proposed meminductor-based chaotic system was implemented using analog integrators, inverters, summers, and multipliers. PSPICE simulation results verified different chaotic characteristics of the proposed circuit with a single change in a resistor value.

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 Generation of 3-D Grid Multi-Scroll Chaotic Attractors Based on Sign Function and Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (12) ◽  
pp. 2145
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng ◽  
Lin Fa
Keyword(s):  
Chaotic System ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Time Shift ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
Simulation Results ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

A three directional (3-D) multi-scroll chaotic attractors based on the Jerk system with nonlinearity of the sine function and sign function is introduced in this paper. The scrolls in the X-direction are generated by the sine function, which is a modified sine function (MSF). In addition, the scrolls in Y and Z directions are generated by the sign function series, which are the superposition of some sign functions with different time-shift values. In the X-direction, the scroll number is adjusted by changing the comparative voltages of the MSF, and the ones in Y and Z directions are regulated by the sign function. The basic dynamics of Lyapunov exponent spectrum, phase diagrams, bifurcation diagram and equilibrium points distribution were studied. Furthermore, the circuits of the chaotic system are designed by Multisim10, and the circuit simulation results indicate the feasibility of the proposed chaotic system for generating chaotic attractors. On the basis of the circuit simulations, the hardware circuits of the system are designed for experimental verification. The experimental results match with the circuit simulation results, this powerfully proves the correctness and feasibility of the proposed system for generating 3-D grid multi-scroll chaotic attractors.

scholarly journals Dynamic Analysis and Circuit Design of a Novel Hyperchaotic System with Fractional-Order Terms

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Abir Lassoued ◽  
Olfa Boubaker
Keyword(s):  
Dynamic Analysis ◽  
Circuit Design ◽  
Fractional Order ◽  
Potential Application ◽  
Complex Dynamics ◽  
Equilibrium Points ◽  
Hyperchaotic System ◽  
Software Simulation ◽  
Simulation Results ◽  
Hyperchaotic Systems

A novel hyperchaotic system with fractional-order (FO) terms is designed. Its highly complex dynamics are investigated in terms of equilibrium points, Lyapunov spectrum, and attractor forms. It will be shown that the proposed system exhibits larger Lyapunov exponents than related hyperchaotic systems. Finally, to enhance its potential application, a related circuit is designed by using the MultiSIM Software. Simulation results verify the effectiveness of the suggested circuit.

scholarly journals A New Fractional-Order Chaotic System with Different Families of Hidden and Self-Excited Attractors

Entropy ◽  
2018 ◽  
Vol 20 (8) ◽  
pp. 564 ◽  
Author(s):  
Jesus Munoz-Pacheco ◽  
Ernesto Zambrano-Serrano ◽  
Christos Volos ◽  
Sajad Jafari ◽  
Jacques Kengne ◽  
...  
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Fractional Order System ◽  
Order System ◽  
Chaotic Attractors ◽  
Equilibrium System ◽  
Hidden Attractors ◽  
Hidden Chaotic Attractor

In this work, a new fractional-order chaotic system with a single parameter and four nonlinearities is introduced. One striking feature is that by varying the system parameter, the fractional-order system generates several complex dynamics: self-excited attractors, hidden attractors, and the coexistence of hidden attractors. In the family of self-excited chaotic attractors, the system has four spiral-saddle-type equilibrium points, or two nonhyperbolic equilibria. Besides, for a certain value of the parameter, a fractional-order no-equilibrium system is obtained. This no-equilibrium system presents a hidden chaotic attractor with a `hurricane’-like shape in the phase space. Multistability is also observed, since a hidden chaotic attractor coexists with a periodic one. The chaos generation in the new fractional-order system is demonstrated by the Lyapunov exponents method and equilibrium stability. Moreover, the complexity of the self-excited and hidden chaotic attractors is analyzed by computing their spectral entropy and Brownian-like motions. Finally, a pseudo-random number generator is designed using the hidden dynamics.

Finding Method and Analysis of Hidden Chaotic Attractors for Plasma Chaotic System From Physical and Mechanistic Perspectives

2020 ◽  
Vol 30 (05) ◽  
pp. 2050072 ◽  
Author(s):  
Yingjuan Yang ◽  
Guoyuan Qi ◽  
Jianbing Hu ◽  
Philippe Faradja
Keyword(s):  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Basin Of Attraction ◽  
The Self ◽  
Numerical Continuation ◽  
Chaotic Attractors ◽  
Phase Portrait Analysis ◽  
The Stability ◽  
Two Parameters ◽  
The Basin Of Attraction

A method for finding hidden chaotic attractors in the plasma system is presented. Using the Routh–Hurwitz criterion, the stability distribution associated with two parameters is identified to find the region around the equilibrium points of the stable nodes, stable focus-nodes, saddles and saddle-foci for the purpose of investigating hidden chaos. A physical interpretation is provided of the stability distribution for each type of equilibrium point. The basin of attraction and parameter region of hidden chaos are identified by excluding the self-excited chaotic attractors of all equilibrium points. Homotopy and numerical continuation are also employed to check whether the basin of chaotic attraction intersects with the neighborhood of a saddle equilibrium. Bifurcation analysis, phase portrait analysis, and basins of different dynamical attraction are used as tools to distinguish visually the self-excited chaotic attractor and hidden chaotic attractor. The Casimir power reflects the error power between the dissipative energy and the energy supplied by the whistler field. It explains physically, analytically, and numerically the conditions that generate the different dynamics, such as sinks, periodic orbits, and chaos.

scholarly journals A New 3D Autonomous Continuous System with Two Isolated Chaotic Attractors and Its Topological Horseshoes

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Ping Zhou ◽  
Meihua Ke
Keyword(s):  
Numerical Computation ◽  
Topological Entropy ◽  
Chaotic System ◽  
Chaotic Attractor ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Continuous System ◽  
Chaotic Attractors ◽  
System A ◽  
Topological Horseshoes

Based on the 3D autonomous continuous Lü chaotic system, a new 3D autonomous continuous chaotic system is proposed in this paper, and there are coexisting chaotic attractors in the 3D autonomous continuous chaotic system. Moreover, there are no overlaps between the coexisting chaotic attractors; that is, there are two isolated chaotic attractors (in this paper, named “positive attractor” and “negative attractor,” resp.). The “positive attractor” and “negative attractor” depend on the distance between the initial points (initial conditions) and the unstable equilibrium points. Furthermore, by means of topological horseshoes theory and numerical computation, the topological horseshoes in this 3D autonomous continuous system is found, and the topological entropy is obtained. These results indicate that the chaotic attractor emerges in the new 3D autonomous continuous system.

scholarly journals Controlling Hyper Chaos with Feedback of Dynamical Variables

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4272-4277 ◽  
Author(s):  
Xiao-Shu Luo ◽  
Bing-Hong Wang
Keyword(s):  
Numerical Simulation ◽  
Hopf Bifurcation ◽  
Theoretical Analysis ◽  
Chaotic Attractors ◽  
Chaotic Circuit ◽  
Controlled System ◽  
Controlling Chaos ◽  
Simulation Results ◽  
System Variables ◽  
Proportional Feedback

We propose a method for controlling chaos and hyper-chaos by applying continuous proportional feedback to the system variables and their derivatives. The method has been applied successfully in six-order coupled Chua's hyper-chaotic circuit system. The theoretical analysis and numerical simulation results show that unstable fixed points embedded in hyper-chaotic attractors can be stabilized and Hopf bifurcation can be observed for the controlled system.

Design of Grid Multiscroll Chaotic Attractors via Transformations

2015 ◽  
Vol 25 (10) ◽  
pp. 1530027 ◽  
Author(s):  
Xingxing Ai ◽  
Kehui Sun ◽  
Shaobo He ◽  
Huihai Wang
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Exponent ◽  
Theoretical Analysis ◽  
Experimental Verification ◽  
Equilibrium Points ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Largest Lyapunov Exponent ◽  
One Dimensional ◽  
Circular Grid

Three transformation approaches for generating grid multiscroll chaotic attractors are presented through theoretical analysis and numerical simulation. Three kinds of grid multiscroll chaotic attractors are generated based on one-dimensional multiscroll Chua system. The dynamics of the multiscroll chaotic attractors are analyzed by means of equilibrium points, eigenvalues, the largest Lyapunov exponent and complexity. As the experimental verification, we implemented the circular grid multiscroll attractor on DSP platform. The simulation and experimental results are consistent well with that of theoretical analysis, and it shows that the design approaches are effective.

MULTISCROLL CHAOTIC ATTRACTORS FROM A MODIFIED COLPITTS OSCILLATOR MODEL

2010 ◽  
Vol 20 (07) ◽  
pp. 2203-2211 ◽  
Author(s):  
BOCHENG BAO ◽  
GUOHUA ZHOU ◽  
JIANPING XU ◽  
ZHONG LIU
Keyword(s):  
Chaotic Attractor ◽  
Equilibrium Points ◽  
Simple Approach ◽  
Oscillator Model ◽  
Chaotic Attractors ◽  
Colpitts Oscillator ◽  
Circuit Realization ◽  
Triangle Function ◽  
Dynamical Characteristics ◽  
Index 2

A simple approach for generating (2N + 1)-scroll chaotic attractor from a modified Colpitts oscillator model is proposed in this paper. The key strategy is to increase the number of index-2 equilibrium points by introducing a triangle function to directly replace the nonlinearity term of Colpitts oscillator model. The dynamical characteristics of the new multiscroll chaotic system are studied comprehensively. A circuit realization structure is introduced and the experimental results demonstrate that (2N + 1)-scroll chaotic attractors can be obtained in practical circuit.

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