scholarly journals Four-Scroll Hyperchaotic Attractor in a Five-Dimensional Memristive Wien Bridge Oscillator: Analysis and Digital Electronic Implementation

2021 ◽  
Vol 2021 ◽  
pp. 1-21
Author(s):  
Gabin Jeatsa Kitio ◽  
Cyrille Ainamon ◽  
Karthikeyan Rajagopal ◽  
Léandre Kamdjeu Kengne ◽  
Sifeu Takougang Kingni ◽  
...  
Keyword(s):  
Time Series ◽  
Basin Of Attraction ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Major Advance ◽  
Bifurcation Diagrams ◽  
Transition To Chaos ◽  
Current Voltage ◽  
Electronic Implementation ◽  
Good Agreement

An electronic implementation of a novel Wien bridge oscillation with antiparallel diodes is proposed in this paper. As a result, we show by using classical nonlinear dynamic tools like bifurcation diagrams, Lyapunov exponent plots, phase portraits, power density spectra graphs, time series, and basin of attraction that the oscillator transition to chaos is operated by intermittency and interior crisis. Some interesting behaviors are found, namely, multistability, hyperchaos, transient chaos, and bursting oscillations. In comparison with some memristor-based oscillators, the plethora of dynamics found in this circuit with current-voltage (i–v) characteristic of diodes mounted in the antiparallel direction represents a major advance in the knowledge of the behavior of this circuit. A suitable microcontroller based design is built to support the numerical findings as these experimental results are in good agreement.

Subharmonic Bifurcations and Transition to Chaos in a Pipe Conveying Fluid under Harmonic Excitation

2013 ◽  
Vol 444-445 ◽  
pp. 791-795
Author(s):  
Yi Xiang Geng ◽  
Han Ze Liu
Keyword(s):  
Chaotic Behavior ◽  
Melnikov Method ◽  
Harmonic Excitation ◽  
Phase Portraits ◽  
Pipe Conveying Fluid ◽  
Bifurcation Diagrams ◽  
Dynamical Behaviors ◽  
Transition To Chaos ◽  
Subharmonic Bifurcations ◽  
Conveying Fluid

The subharmonic and chaotic behavior of a two end-fixed fluid conveying pipe whose base is subjected to a harmonic excitation are investigated. Melnikov method is applied for the system, and Melnikov criterions for subharmonic and homoclinic bifurcations are obtained analytically. The numerical simulations (including bifurcation diagrams, maximal Lyapunov exponents, phase portraits and Poincare map) confirm the analytical predictions and exhibit the complicated dynamical behaviors.

Dynamic Analysis of the Effect of Quitting Smoking Applications on Smoking Cessation

2020 ◽  
pp. 74-94
Author(s):  
A. George Maria Selvam ◽  
Mary Jacintha
Keyword(s):  
Time Series ◽  
Smoking Cessation ◽  
Linear System ◽  
Dynamic Analysis ◽  
Dynamical Analysis ◽  
Phase Portraits ◽  
System Of Differential Equations ◽  
Bifurcation Diagrams ◽  
Quitting Smoking ◽  
Non Linear System

In this chapter, the authors considered a smoking cessation model formulated with a non-linear system of differential equations and obtained the continuous fractional order model and through discretization its discrete form to study the effectiveness of quitting smoking applications in giving up smoking. The existence of smoking free equilibria and smoking present equilibria are discussed, and the dynamical analysis of these two equilibria is put forward with the assistance of the smoking generation number. The numerical simulations aided by time series, phase portraits, and bifurcation diagrams confirm the results that are obtained analytically.

NONINVERTIBLE TWO-DIMENSIONAL MAPS ARISING IN RADIOPHYSICS

1994 ◽  
Vol 04 (02) ◽  
pp. 383-400 ◽  
Author(s):  
VLADIMIR MAISTRENKO ◽  
YURI MAISTRENKO ◽  
IRINA SUSHKO
Keyword(s):  
Period Doubling ◽  
Phase Portraits ◽  
Two Dimensional ◽  
Bifurcation Diagrams ◽  
One Dimensional ◽  
Transition To Chaos ◽  
Nonlinear Amplifiers ◽  
Noninvertible Maps ◽  
Triangular Maps ◽  
Two Parameter

We study a two-parameter family of noninvertible maps modeling a generator which consists of two identical nonlinear amplifiers and two delay circuits. The ratio of the delays determines the dimension of the map and our attention is mainly on the two-dimensional case. The mechanism of transition to chaos appears to be one-dimensional and is realized through a period-doubling cascade. To get a more complete description we suggest the use of so-called triangular maps. Phase portraits are constructed for some types of model triangular maps. Also we get one- and two-dimensional bifurcation diagrams for the maps considered and attractor basins in the case of multistability using computer simulation.

scholarly journals Parameter-Independent Dynamical Behaviors in Memristor-Based Wien-Bridge Oscillator

2017 ◽  
Vol 2017 ◽  
pp. 1-13 ◽  
Author(s):  
Ning Wang ◽  
Bocheng Bao ◽  
Tao Jiang ◽  
Mo Chen ◽  
Quan Xu
Keyword(s):  
Chaotic Attractor ◽  
Initial Conditions ◽  
System Model ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Chaotic Oscillator ◽  
Initial Condition ◽  
Bifurcation Diagrams ◽  
System Parameters ◽  
Dynamical Behaviors

This paper presents a novel memristor-based Wien-bridge oscillator and investigates its parameter-independent dynamical behaviors. The newly proposed memristive chaotic oscillator is constructed by linearly coupling a nonlinear active filter composed of memristor and capacitor to a Wien-bridge oscillator. For a set of circuit parameters, phase portraits of a double-scroll chaotic attractor are obtained by numerical simulations and then validated by hardware experiments. With a dimensionless system model and the determined system parameters, the initial condition-dependent dynamical behaviors are explored through bifurcation diagrams, Lyapunov exponents, and phase portraits, upon which the coexisting infinitely many attractors and transient chaos related to initial conditions are perfectly offered. These results are well verified by PSIM circuit simulations.

Extreme Multistability and Complex Dynamics of a Memristor-Based Chaotic System

2020 ◽  
Vol 30 (08) ◽  
pp. 2030019
Author(s):  
Hui Chang ◽  
Yuxia Li ◽  
Guanrong Chen ◽  
Fang Yuan
Keyword(s):  
Complex Dynamics ◽  
Hysteresis Loops ◽  
Digital Signal ◽  
Phase Portraits ◽  
Transient Chaos ◽  
Bifurcation Diagrams ◽  
Extreme Multistability ◽  
Memristive System ◽  
Autonomous Differential Equations ◽  
Pinched Hysteresis

A memristor with coexisting pinched hysteresis loops and twin local activity domains is presented and analyzed, with an emulator being designed and applied to the classic Chua’s circuit to replace the diode. The memristive system is modeled with four coupled first-order autonomous differential equations, which has three equilibria determined by three static equilibria of the memristor but not controlled by the system parameters. The complex dynamics of the system are analyzed by using compound coexisting bifurcation diagrams, Lyapunov exponent spectra and phase portraits, including point attractors, limit cycles, symmetrical chaotic attractors and their blasting, extreme multistability, state-switching without parameter, and transient chaos. Of particular surprise is that the extreme multistability of the system is hidden and symmetrically distributed. It is found that the existence of transient chaos in the specified parameter domain is determined by using bifurcation diagrams within different time durations and Lyapunov exponents with chaotic sequences. Finally, the symmetrical chaotic attractor and the system blasting are verified by digital signal processing experiments, which are consistent with the numerical analysis.

Dynamics of SC-CNN Based Variant of MLC Circuit: An Experimental Study

2014 ◽  
Vol 24 (02) ◽  
pp. 1430008 ◽  
Author(s):  
P. S. Swathy ◽  
K. Thamilmaran
Keyword(s):  
Neural Network ◽  
Experimental Study ◽  
Time Series ◽  
Power Spectra ◽  
Cellular Neural Network ◽  
Phase Portraits ◽  
Onset Of Chaos ◽  
Experimental Time Series ◽  
The Stability ◽  
Good Agreement

In this paper, a State Controlled Cellular Neural Network (SC-CNN) based variant of Murali–Lakshmanan–Chua (MLCV) circuit is presented. The proposed system is modeled by using a suitable connection of two simple state controlled generalized CNN cells, while the stability of the circuit is studied by determining the eigenvalues of the stability matrices, the dynamics as well as onset of chaos, torus and bifurcation have been investigated through laboratory hardware experiments and numerical analysis of the generalized SC-CNN equations. The experimental results such as phase portraits, Poincaré map and power spectra are in good agreement with those of numerical computations. We further validate our findings with data obtained from both experimental time series observations and numerical simulations and discuss "0-1 test" for distinguishing quasiperiodicity and chaoticity, which successfully detects the transition. The results obtained are quite satisfactory and significant.

A New Dynamical Circuit Based on CCII+, Physical Implementation and Synchronization

2021 ◽  
pp. 2150289
Author(s):  
Ahmet Can Özçelik ◽  
Zehra Gülru Çam Taşkiran
Keyword(s):  
Secure Communication ◽  
Analog Circuit ◽  
Synthesis Method ◽  
Cost Effective ◽  
Parallel Synthesis ◽  
Phase Portraits ◽  
Communication Studies ◽  
Mathematical Analyses ◽  
Electronic Implementation ◽  
Good Agreement

In this study, a second-generation positive current conveyor (CCII+)-based analog circuit is proposed for the electronic implementation of a different dynamical system which is an adaptation of the chaotic Lorenz differential equation set. The proposed circuit is more cost-effective and contains less active and passive elements than the circuit obtained by applying the classical parallel synthesis method with opamps. Mathematical analyses and SPICE simulations are performed for chaotic phase portraits and bifurcation diagrams. The proposed dynamical circuit is implemented on the board by using commercially available active and passive elements on the market and an experimental study is conducted. In order to demonstrate the usability of this proposed circuit in secure communication studies, three different synchronization methods are applied and one of them is implemented. The obtained experimental results are in good agreement with the mathematical analysis and simulation results.

scholarly journals Complexity of a Discrete-Time Predator-Prey Model Involving Prey Refuge Proportional to Predator

2022 ◽  
Vol 4 (1) ◽  
pp. 50-63
Author(s):  
P. K. Santra ◽  
Hasan S. Panigoro ◽  
G. S. Mahapatra
Keyword(s):  
Time Series ◽  
Discrete Time ◽  
Local Stability ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Predator Density ◽  
Prey Refuge ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical simulations consisting of bifurcation diagrams, phase portraits, and time-series are given to support analytical findings. The occurrence of chaotic solutions are also presented by showing the Lyapunov exponent while some parameters are varied.

Point Contact Current Voltage Measurements of 4H-SiC Samples with Different Doping Profiles

2017 ◽  
Vol 897 ◽  
pp. 287-290 ◽  
Author(s):  
Matthias Kocher ◽  
Michael Niebauer ◽  
Mathias Rommel ◽  
Volker Haeublein ◽  
Anton J. Bauer
Keyword(s):  
Epitaxial Layer ◽  
Depth Profile ◽  
Point Contact ◽  
Surface Preparation ◽  
Epitaxial Layers ◽  
Depth Profiles ◽  
Current Voltage ◽  
Measured Resistance ◽  
Doping Profiles ◽  
Good Agreement

Point contact current voltage (PCIV) measurements were performed on 4H-SiC samples, both for n- an p-doped epitaxial layers as well as samples with rather shallow doping profiles realized by N- or Al-implantation in a range from 1016 cm-3 to 1019 cm-3. Surface preparation and measurement parameters were investigated in order to determine their influence on the measured resistance profiles. Furthermore depth profile measurements were performed on both an epitaxial layer as well as on implanted samples. These depth profiles could be measured reproducibly and showed good agreement with expected profiles for Al-implanted samples as well as for epitaxial layer whereas for N-implanted samples deviations between measured and expected profiles could be observed. It could be proven that PCIV profiling technique is a promising method for characterizing doped profiles in 4H-SiC, especially on Al-implanted samples.

scholarly journals Chaos and Control in Coronary Artery System

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Yanxiang Shi
Keyword(s):  
Coronary Artery ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Melnikov Method ◽  
Phase Portraits ◽  
Bifurcation Diagrams ◽  
Nonlinear Dynamical ◽  
The Road ◽  
Two Systems ◽  
And Control

Two types of coronary artery system N-type and S-type, are investigated. The threshold conditions for the occurrence of Smale horseshoe chaos are obtained by using Melnikov method. Numerical simulations including phase portraits, potential diagram, homoclinic bifurcation curve diagrams, bifurcation diagrams, and Poincaré maps not only prove the correctness of theoretical analysis but also show the interesting bifurcation diagrams and the more new complex dynamical behaviors. Numerical simulations are used to investigate the nonlinear dynamical characteristics and complexity of the two systems, revealing bifurcation forms and the road leading to chaotic motion. Finally the chaotic states of the two systems are effectively controlled by two control methods: variable feedback control and coupled feedback control.

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