Nine-Dimensional Eight-Order Chaotic System and its Circuit Implementation

2014 ◽  
Vol 716-717 ◽  
pp. 1346-1351
Author(s):  
Jian Liang Zhu ◽  
Jiang Dong ◽  
Hua Qiang Gao
Keyword(s):  
Chaotic System ◽  
Chaos Theory ◽  
High Dimensional ◽  
Chaotic Attractors ◽  
Higher Dimension ◽  
Matlab Simulation ◽  
Circuit Implementation ◽  
Dynamical Behaviors ◽  
Simulation Results ◽  
Hardware Circuit

The chaotic characteristics of high-dimensional chaotic system are more complex, so the design of chaotic system with higher dimension has become a leading subject of chaos theory. In this paper, we constructed a nine-dimensional eight-order chaotic system. Matlab simulation of system is performed and Lyapunov exponents are figured out, which proved more complex dynamical behaviors. And the corresponding hardware circuit is designed. Multisim simulation results of the circuit coincide with Matlab simulation of the system completely, showing the same chaotic attractors. The consistent results verified the realizability of system. Therefore, the system can provide a more secure encryption source for information encryption.

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 Circuit Implementation Synchronization between Two Modified Fractional-Order Lorenz Chaotic Systems via a Linear Resistor and Fractional-Order Capacitor in Parallel Coupling

2021 ◽  
Vol 2021 ◽  
pp. 1-8 ◽  
Author(s):  
Juan Liu ◽  
Xuefeng Cheng ◽  
Ping Zhou
Keyword(s):  
Fractional Order ◽  
Chaotic System ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Electronic Circuit ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
Synchronization Scheme

In this study, a modified fractional-order Lorenz chaotic system is proposed, and the chaotic attractors are obtained. Meanwhile, we construct one electronic circuit to realize the modified fractional-order Lorenz chaotic system. Most importantly, using a linear resistor and a fractional-order capacitor in parallel coupling, we suggested one chaos synchronization scheme for this modified fractional-order Lorenz chaotic system. The electronic circuit of chaos synchronization for modified fractional-order Lorenz chaotic has been given. The simulation results verify that synchronization scheme is viable.

scholarly journals Circuit Implementation and Antisynchronization of an Improved Lorenz Chaotic System

2016 ◽  
Vol 2016 ◽  
pp. 1-12
Author(s):  
Li Xiong ◽  
Yan-Jun Lu ◽  
Qi-Meng Zhang ◽  
Zhi-Yu Zhang
Keyword(s):  
Chaotic System ◽  
Optimization Design ◽  
Lorenz System ◽  
Circuit Implementation ◽  
Electronic Components ◽  
Comprehensive Performance ◽  
Lorenz Chaotic System ◽  
Simulation Results ◽  
Hardware Circuit ◽  
Theoretical Analyses

An improved Lorenz chaotic system is proposed, making it into a circuit which is easy to be implemented by using some basic electronic components. The antisynchronization error systems can be asymptotically stabilized at the origin with three different methods which are proposed to control the improved Lorenz system. Theoretical analyses and simulation results are given to demonstrate the feasibility and effectiveness of these proposed schemes. Then the hardware circuit for the proposed Lorenz system is implemented by repeated optimization design. Experimental results show that the circuit has good comprehensive performance.

scholarly journals A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

Inventions ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 49
Author(s):  
Zain-Aldeen S. A. Rahman ◽  
Basil H. Jasim ◽  
Yasir I. A. Al-Yasir ◽  
Raed A. Abd-Alhameed ◽  
Bilal Naji Alhasnawi
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Chaotic System ◽  
Real World ◽  
Experimental Results ◽  
Chaotic Attractors ◽  
State Variables ◽  
Digital Implementation ◽  
Dynamical Behaviors ◽  
Real World Applications

In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

scholarly journals Low Model Analysis and Synchronous Simulation of the Wave Mechanics

2016 ◽  
Vol 2016 ◽  
pp. 1-13
Author(s):  
Wenyuan Duan ◽  
Heyuan Wang ◽  
Meng Kan
Keyword(s):  
Numerical Simulation ◽  
Lyapunov Function ◽  
Chaotic System ◽  
Invariant Set ◽  
Positive Definite ◽  
Chaotic Attractors ◽  
Wave Mechanics ◽  
Wave Dynamics ◽  
Simulation Results ◽  
Positive Invariant Set

The dynamic behavior of a chaotic system in the internal wave dynamics and the problem of the tracing and synchronization are investigated, and the numerical simulation is carried out in this paper. The globally exponentially attractive set and positive invariant set of the chaotic system are studied via constructing the positive definite and radial unbounded Lyapunov function. There are no equilibrium positions, periodic solutions, quasi-period motions, wandering recovering motions, and other chaotic attractors of the system out of the globally exponentially attractive set. Strange attractors can only locate in the globally exponentially attractive set. A feedback controller is designed for the chaotic system to realize the control of the unstable point. The second method of Lyapunov is used to discuss theoretically the rationality of the design of the controller. The driving-response synchronization method is used to realize the globally exponential synchronization. The numerical simulation is carried out by MATLAB software, and the simulation results show that the method is effective.

A NEW CHAOTIC SYSTEM AND BEYOND: THE GENERALIZED LORENZ-LIKE SYSTEM

2004 ◽  
Vol 14 (05) ◽  
pp. 1507-1537 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN ◽  
DAIZHAN CHENG
Keyword(s):  
Chaotic System ◽  
Chaotic Attractor ◽  
Three Dimensional ◽  
Chaotic Attractors ◽  
Compound Structure ◽  
Constant Input ◽  
New Class ◽  
Dynamical Behaviors ◽  
Generalized Lorenz System ◽  
New Chaotic System

This article introduces a new chaotic system of three-dimensional quadratic autonomous ordinary differential equations, which can display (i) two 1-scroll chaotic attractors simultaneously, with only three equilibria, and (ii) two 2-scroll chaotic attractors simultaneously, with five equilibria. Several issues such as some basic dynamical behaviors, routes to chaos, bifurcations, periodic windows, and the compound structure of the new chaotic system are then investigated, either analytically or numerically. Of particular interest is the fact that this chaotic system can generate a complex 4-scroll chaotic attractor or confine two attractors to a 2-scroll chaotic attractor under the control of a simple constant input. Furthermore, the concept of generalized Lorenz system is extended to a new class of generalized Lorenz-like systems in a canonical form. Finally, the important problems of classification and normal form of three-dimensional quadratic autonomous chaotic systems are formulated and discussed.

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 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.

Six-Dimensional Chaotic System and its Circuit Implementation

2011 ◽  
Vol 255-260 ◽  
pp. 2018-2022 ◽  
Author(s):  
Jian Liang Zhu ◽  
Yu Jing Wang ◽  
Shou Qiang Kang
Keyword(s):  
Numerical Simulation ◽  
Power Spectrum ◽  
Chaotic System ◽  
Time Domain ◽  
Circuit Simulation ◽  
System Simulation ◽  
Practical Significance ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Product Term

In order to generate complex chaotic attractors, a six-dimensional chaotic system is designed, which contains six parameters and each equation contains a nonlinear product term. When its parameters satisfy certain conditions, the system is chaotic. By Matlab numerical simulation, chaotic attractor and relevant Lyapunov exponents spectrum can be obtained, which validates that the system is chaotic. And, time domain waveform and power spectrum are shown. Finally, the implementation circuit of this system is designed, and circuit simulation can be done by using Multisim. Circuit simulation result is identical to system simulation completely. The circuit has a practical significance in secrecy communication and correlative fields.

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