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.

SYMMETRICAL DYNAMICS OF CURRENT-MODE CONTROLLED SWITCHING DC-DC CONVERTERS

2012 ◽  
Vol 22 (01) ◽  
pp. 1250008 ◽  
Author(s):  
GUOHUA ZHOU ◽  
JIANPING XU ◽  
BOCHENG BAO
Keyword(s):  
Current Mode ◽  
Parameter Variation ◽  
Phase Portraits ◽  
Circuit Parameter ◽  
Bifurcation Diagrams ◽  
Boost Converters ◽  
Controlled Switching ◽  
Dynamical Behaviors ◽  
Variation Range ◽  
Simulation Results

Peak Current-Mode (PCM) and Valley Current-Mode (VCM) controlled switching dc-dc converters have symmetrical dynamical behaviors within a wide circuit parameter variation range. To investigate the symmetrical dynamical behaviors between PCM and VCM controlled switching dc-dc converters, the iterative map models and inductor current borderlines that exist in the bifurcation diagrams of both PCM and VCM controlled buck, boost, and buck-boost converters are established. The research results of bifurcation behaviors indicate that the bifurcation diagrams of PCM and VCM controlled switching dc-dc converters have symmetrical dynamical behaviors corresponding to a symmetrical point (SP). The simulation results show that time-domain waveforms of PCM and VCM controlled switching dc-dc converters working in periodic orbits have symmetrical axis and SP, and the SP also exists in corresponding phase portraits. Experimental results are given to verify the analysis and simulation results in this paper.

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 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 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.

Generating Four-Wing Hyperchaotic Attractor and Two-Wing, Three-Wing, and Four-Wing Chaotic Attractors in 4D Memristive System

2017 ◽  
Vol 27 (02) ◽  
pp. 1750027 ◽  
Author(s):  
Ling Zhou ◽  
Chunhua Wang ◽  
Lili Zhou
Keyword(s):  
Chaotic System ◽  
Three Dimensional ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Hyperchaotic System ◽  
Multiple Attractors ◽  
System A ◽  
Dynamical Behaviors ◽  
Memristive System ◽  
Line Of Equilibria

By adding only one smooth flux-controlled memristor into a three-dimensional (3D) pseudo four-wing chaotic system, a new real four-wing hyperchaotic system is constructed in this paper. It is interesting to see that this new memristive chaotic system can generate a four-wing hyperchaotic attractor with a line of equilibria. Moreover, it can generate two-, three- and four-wing chaotic attractors with the variation of a single parameter which denotes the strength of the memristor. At the same time, various coexisting multiple attractors (e.g. three-wing attractors, four-wing attractors and attractors with state transition under the same system parameters) are observed in this system, which means that extreme multistability arises. The complex dynamical behaviors of the proposed system are analyzed by Lyapunov exponents (LEs), phase portraits, Poincaré maps, and time series. An electronic circuit is finally designed to implement the hyperchaotic memristive system.

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.

GENERATION OF MULTI-WING CHAOTIC ATTRACTORS FROM A LORENZ-LIKE SYSTEM

2013 ◽  
Vol 23 (09) ◽  
pp. 1350152 ◽  
Author(s):  
QIANG LAI ◽  
ZHI-HONG GUAN ◽  
YONGHONG WU ◽  
FENG LIU ◽  
DING-XUE ZHANG
Keyword(s):  
Theoretical Analysis ◽  
Chaotic System ◽  
Chaotic Attractors ◽  
Initial Value ◽  
Simulation Results ◽  
Switching Method

In this paper, two methods are proposed to construct multi-wing chaotic attractors based on a Lorenz-like autonomous chaotic system. The first is switching method which can directly multiply the wings of the system without segment linearization of the system. The second is coordinate transition method which is related to the initial value of the system. Moreover, theoretical analysis and simulation results show the effectiveness of these two methods.

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.

CONTROLLING THE UNCERTAIN MULTI-SCROLL CRITICAL CHAOTIC SYSTEM WITH INPUT NONLINEAR USING SLIDING MODE CONTROL

2009 ◽  
Vol 23 (16) ◽  
pp. 2021-2034 ◽  
Author(s):  
XINGYUAN WANG ◽  
DA LIN ◽  
ZHANJIE WANG
Keyword(s):  
Chaotic System ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Dead Zone ◽  
Variable Structure ◽  
Sliding Mode Controller ◽  
Global Stabilization ◽  
Structure Control ◽  
Control Scheme ◽  
Simulation Results

In this paper, control of the uncertain multi-scroll critical chaotic system is studied. According to variable structure control theory, we design the sliding mode controller of the uncertain multi-scroll critical chaotic system, which contains sector nonlinearity and dead zone inputs. For an arbitrarily given equilibrium point of the uncertain multi-scroll chaotic system, we achieve global stabilization for the equilibrium points. Particularly, a class of proportional integral (PI) switching surface is introduced for determining the convergence rate. Furthermore, the proposed control scheme can be extended to complex multi-scroll networks. Finally, simulation results are presented to demonstrate the effectiveness of the proposed control scheme.

scholarly journals Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xia Huang ◽  
Zhen Wang ◽  
Yuxia Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Nonlinear Dynamics And Chaos

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

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