scholarly journals Generation of Multi-Scroll Chaotic Attractors from a Jerk Circuit with a Special Form of a Sine Function

Electronics ◽  
2020 ◽  
Vol 9 (5) ◽  
pp. 842
Author(s):  
Pengfei Ding ◽  
Xiaoyi Feng
Keyword(s):  
Chaotic System ◽  
Special Form ◽  
Electronic Circuit ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Sine Function ◽  
Sign Function ◽  
System Parameters ◽  
Left And Right

A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are infinite equilibrium points in this system, the scroll number of the generated chaotic attractors is certain under appropriate system parameters. The dynamical properties of the proposed chaotic system are studied through Lyapunov exponents, phase portraits, and bifurcation diagrams. It is found that the scroll number of the chaotic system in the left and right part of the x-y plane can be determined arbitrarily by adjusting the values of the parameters in the SFSF, and the size of attractors is dominated by the frequency of the SFSF. Finally, an electronic circuit of the proposed chaotic system is implemented on Pspice, and the simulation results of electronic circuit are in agreement with the numerical ones.

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 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.

Stability and Hopf bifurcation analysis of a new four-dimensional hyper-chaotic system

2020 ◽  
Vol 34 (29) ◽  
pp. 2050327
Author(s):  
Liangqiang Zhou ◽  
Ziman Zhao ◽  
Fangqi Chen
Keyword(s):  
Hopf Bifurcation ◽  
Chaotic System ◽  
Bifurcation Theory ◽  
Center Manifold ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Local Dynamic ◽  
Chaotic Motions ◽  
System Parameters ◽  
Lyapunov Coefficient

With both analytical and numerical methods, local dynamic behaviors including stability and Hopf bifurcation of a new four-dimensional hyper-chaotic system are studied in this paper. All the equilibrium points and their stability conditions are obtained with the Routh–Hurwitz criterion. It is shown that there may exist one, two, or three equilibrium points for different system parameters. Via Hopf bifurcation theory, parameter conditions leading to Hopf bifurcation is presented. With the aid of center manifold and the first Lyapunov coefficient, it is also presented that the Hopf bifurcation is supercritical for some certain parameters. Finally, numerical simulations are given to confirm the analytical results and demonstrate the chaotic attractors of this system. It is also shown that the system may evolve chaotic motions through periodic bifurcations or intermittence chaos while the system parameters vary.

scholarly journals A Chaotic System with Infinite Equilibria and Its S-Box Constructing Application

2018 ◽  
Vol 8 (11) ◽  
pp. 2132 ◽  
Author(s):  
Xiong Wang ◽  
Akif Akgul ◽  
Unal Cavusoglu ◽  
Viet-Thanh Pham ◽  
Duy Vo Hoang ◽  
...  
Keyword(s):  
Chaotic System ◽  
Infinite Number ◽  
Electronic Circuit ◽  
Equilibrium Points ◽  
Chaotic Attractors ◽  
Performance Tests ◽  
Generation Algorithm ◽  
Performance Results ◽  
Number Of Equilibria ◽  
Line Equilibrium

Systems with many equilibrium points have attracted considerable interest recently. A chaotic system with a line equilibrium has been studied in this work. The system has infinite equilibria and exhibits coexisting chaotic attractors. The system with an infinite number of equilibria has been realized by an electronic circuit, which confirms the feasibility of the system. Based on such a system, we have developed a new S-Box generation algorithm. With the developed algorithm, two new S-Boxes are produced. Performance tests of S-Boxes are performed. The tests have shown that proposed S-Boxes have good performance results.

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.

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.

scholarly journals A New 3-D Chaotic System with Conch-Shaped Equilibrium Curve and its Circuit Implementation

2018 ◽  
Vol 7 (3) ◽  
pp. 1410 ◽  
Author(s):  
Mustafa Mamat ◽  
Sundarapandian Vaidyanathan ◽  
Aceng Sambas ◽  
Mohamad Afendee ◽  
Sivaperumal Sampath ◽  
...  
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Phase Portraits ◽  
Equilibrium Curve ◽  
Closed Curves ◽  
New Chaotic System ◽  
Electronic Circuit Simulation

This paper reports the finding a new chaotic system with a conch-shaped equilibrium curve. The proposed system is a new addition to existing chaotic systems with closed curves of equilibrium points in the literature. Lyapunov exponents of the new chaotic system are studiedfor verifying chaos properties and phase portraits of the new system via MATLAB are unveiled. An electronic circuit simulation of the new chaotic system with conch-shaped equilibrium curve is shown using MultiSIM to check the model feasibility.

A Unified Chaotic System with Various Coexisting Attractors

2021 ◽  
Vol 31 (01) ◽  
pp. 2150013
Author(s):  
Qiang Lai
Keyword(s):  
Chaotic System ◽  
Equilibrium Points ◽  
Sine Function ◽  
Coexisting Attractors ◽  
Dynamic Behaviors ◽  
Multiple Zeros ◽  
Unified Chaotic System

This article presents a unified four-dimensional autonomous chaotic system with various coexisting attractors. The dynamic behaviors of the system are determined by its special nonlinearities with multiple zeros. Two cases of nonlinearities with sine function of the system are discussed. The symmetrical coexisting attractors, asymmetrical coexisting attractors and infinitely many coexisting attractors in the system are numerically demonstrated. This shows that such a system has an ability to produce abundant coexisting attractors, depending on the number of equilibrium points determined by nonlinearities.

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.

The Effects of a Constant Excitation Force on the Dynamics of an Infinite-Equilibrium Chaotic System Without Linear Terms: Analysis, Control and Circuit Simulation

2020 ◽  
Vol 30 (15) ◽  
pp. 2050234
Author(s):  
L. Kamdjeu Kengne ◽  
Z. Tabekoueng Njitacke ◽  
J. R. Mboupda Pone ◽  
H. T. Kamdem Tagne
Keyword(s):  
Chaotic System ◽  
Analog Circuit ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Nonlinear Behavior ◽  
Basins Of Attraction ◽  
Phase Portraits ◽  
Unique Contribution ◽  
Chaotic Signals ◽  
Excitation Force

In this paper, the effects of a bias term modeling a constant excitation force on the dynamics of an infinite-equilibrium chaotic system without linear terms are investigated. As a result, it is found that the bias term reduces the number of equilibrium points (transition from infinite-equilibria to only two equilibria) and breaks the symmetry of the model. The nonlinear behavior of the system is highlighted in terms of bifurcation diagrams, maximal Lyapunov exponent plots, phase portraits, and basins of attraction. Some interesting phenomena are found including, for instance, hysteretic dynamics, multistability, and coexisting bifurcation branches when monitoring the system parameters and the bias term. Also, we demonstrate that it is possible to control the offset and amplitude of the chaotic signals generated. Compared to some few cases previously reported on systems without linear terms, the plethora of behaviors found in this work represents a unique contribution in comparison with such type of systems. A suitable analog circuit is designed and used to support the theoretical analysis via a series of Pspice simulations.

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