Generation and Circuit Implementation of Multi-Scroll Chaotic Attractors with Controllable Direction

2014 ◽  
Vol 513-517 ◽  
pp. 4559-4562
Author(s):  
Xiao Wen Luo ◽  
Chun Hua Wang
Keyword(s):  
Lyapunov Exponent ◽  
Control Function ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Relative Coefficient ◽  
Jerk System ◽  
Lyapunov Exponent Spectrum

An approach for generating multi-scroll chaotic attractors with controllable direction in one plane is proposed. Firstly, an appropriate nonlinear function is selected to control the number and direction of multi-scroll chaotic attractors in the three-order Jerk system. Then, we add new control function to Jerk system and observe Lyapunov exponent spectrum of relative coefficient and the change of equilibrium points. Different multi-scroll chaotic attractors with controllable direction are generated by adjusting the coefficient of the control function in a plane. The implementation of circuit verifies the feasibility of this method.

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 Comparison of Complexity of the Switchable Chaotic Systems and its FPGA Implementation

2021 ◽  
Author(s):  
Shaohui Yan ◽  
Qiyu Wang
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Equilibrium Points ◽  
Nonlinear Function ◽  
Order System ◽  
Integer Order ◽  
Coexistence Of Attractors ◽  
Field Programmable ◽  
Lyapunov Exponent Spectrum

Abstract A four-dimensional chaotic system with complex dynamical properties is constructed via introducing a nonlinear function term. The paper assesses complexity of the system employing equilibrium points, Lyapunov exponent spectrum and bifurcation model. Specially, the coexisting Lyapunov exponent spectrum and the coexisting bifurcation validate the coexistence of attractors. The corresponding complexity characteristics of the system can be analyzed by using C0 and spectral entropy(SE) complexity algorithms, and the most complicated integer-order system is obtained. Furthermore, the circuit which can switch the chaotic attractors is implemented. It is worth noting that the more sophisticated parameters are received by comparing the complexity of the most complicated integer-order chaotic system with corresponding fractional-order chaotic system. Finally, the results of simulation model built in the MATLAB are the same as the hardware verified on the Field-Programmable Gate Array(FPGA) platform, which verify the feasibility of the system.

Generating Multiple Chaotic Attractors from Sprott B System

2016 ◽  
Vol 26 (11) ◽  
pp. 1650177 ◽  
Author(s):  
Qiang Lai ◽  
Shiming Chen
Keyword(s):  
Lyapunov Exponent ◽  
Function Method ◽  
Polynomial Function ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Nonlinear Phenomenon ◽  
Bifurcation Diagrams ◽  
Initial Values ◽  
Index 2 ◽  
Lyapunov Exponent Spectrum

Multiple chaotic attractors, implying several independent chaotic attractors generated simultaneously in a system from different initial values, are a very interesting and important nonlinear phenomenon, but there are few studies that have previously addressed it to our best knowledge. In this paper, we propose a polynomial function method for generating multiple chaotic attractors from the Sprott B system. The polynomial function extends the number of index-2 saddle foci, which determines the emergence of multiple chaotic attractors in the system. The analysis of the equilibria is presented. Two coexisting chaotic attractors, three coexisting chaotic attractors and four coexisting chaotic attractors are investigated for verifying the effectiveness of the method. The chaotic characteristics of the attractors are shown by bifurcation diagrams, Lyapunov exponent spectrum and phase portraits.

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.

scholarly journals Symmetric Coexisting Attractors in a Novel Memristors-Based Chuas Chaotic System

2021 ◽  
Author(s):  
Shaohui Yan ◽  
Zhenlong Song ◽  
Wanlin Shi
Keyword(s):  
Lyapunov Exponent ◽  
Chaotic System ◽  
Analog Circuits ◽  
Complex Dynamics ◽  
Chaotic Attractors ◽  
Coexisting Attractors ◽  
Initial Value ◽  
Field Programmable ◽  
A Charge ◽  
Lyapunov Exponent Spectrum

This paper introduces a charge-controlled memristor based on the classical Chuas circuit. It also designs a novel four-dimensional chaotic system and investigates its complex dynamics, including phase portrait, Lyapunov exponent spectrum, bifurcation diagram, equilibrium point, dissipation and stability. The system appears as single-wing, double-wings chaotic attractors and the Lyapunov exponent spectrum of the system is symmetric with respect to the initial value. In addition, symmetric and asymmetric coexisting attractors are generated by changing the initial value and parameters. The findings indicate that the circuit system is equipped with excellent multi-stability. Finally, the circuit is implemented in Field Programmable Gate Array (FPGA) and analog circuits.

Circuit Implementation of Multiscroll Chaotic Attractors Generated Using Step Function

2015 ◽  
Vol 25 (12) ◽  
pp. 1550160
Author(s):  
Yingjie Ma ◽  
Hua Jiang ◽  
Lei Ju
Keyword(s):  
Time Domain ◽  
Nonlinear Function ◽  
Step Function ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
New Chaotic System ◽  
The Time Domain ◽  
Hardware Circuit ◽  
The Physical Realization

A new chaotic system is proposed to generate multiscroll chaotic attractors. The major method used is for the step function to act as a nonlinear function. To prove that the proposed system can generate multiscroll chaotic attractors, the equilibrium point, the time domain waveform and the phase diagram of the proposed system are calculated. Finally, the design of the hardware circuit produces experimental results at a maximum of 8-scroll hardware. Theoretical analysis, simulation and hardware experimental results are fully matched, which further proves the existence of the proposed system and the physical realization. This provides the possibility for future applications in engineering.

A Simple Method for Generating Mirror Symmetry Composite Multiscroll Chaotic Attractors

2020 ◽  
Vol 30 (11) ◽  
pp. 2050220
Author(s):  
Xuenan Peng ◽  
Yicheng Zeng
Keyword(s):  
Lyapunov Exponent ◽  
Mirror Symmetry ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Attractors ◽  
Simple Method ◽  
Dynamical Behaviors ◽  
The Lorenz System ◽  
Lyapunov Exponent Spectrum ◽  
New System

For further increasing the complexity of chaotic attractors, a new method for generating Mirror Symmetry Composite Multiscroll Chaotic Attractors (MSCMCA) is proposed. We take the Lorenz system as an example to explain the mechanism of the method. Firstly, by varying the signs and magnitudes of the nonlinear terms, the Lorenz system generates symmetrical attractors and different-magnitude attractors, respectively. Secondly, a modified Lorenz system is constructed by imposing several unified multilevel-logic pulse signals to the Lorenz system. The new system generates a novel chaotic attractor consisting of two pairs of different-magnitude symmetrical attractors. By adjusting the parameters of the pulse signals, the modified Lorenz system can also be controlled to generate novel grid multiscroll chaotic attractors, namely MSCMCA. Several dynamical behaviors of the new system are shown by equilibria analysis and Lyapunov exponent spectrum. Moreover, the method can be applied to other chaotic systems. Finally, a circuit of the modified Lorenz system is designed by Multisim software, and the simulation result proves the effectiveness of the method.

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