scholarly journals A Simple Chaotic Wien Bridge Oscillator with a Fractional-Order Memristor and Its Combination Synchronization for Efficient Antiattack Capability

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Anitha Karthikeyan ◽  
Karthikeyan Rajagopal ◽  
Victor Kamdoum Tamba ◽  
Girma Adam ◽  
Ashokkumar Srinivasan
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
Combination Synchronization ◽  
Response System ◽  
Recent Interest ◽  
Wide Range ◽  
Dynamical Properties ◽  
Drive Systems ◽  
Synchronization Scheme ◽  
Fractional Orders

Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them in detail. The oscillator is then realized using off-the-shelf components, and the results are compared with that of the numerical results. A combination synchronization scheme is proposed which uses more than one driver systems to synchronize with one response system. Indeed, we use two different techniques where the first one consists of splitting the transmitted signals into two parts where each part is loaded in different drive systems, while the second one consists of dividing time into different intervals and loading the signals in different drive systems. Such techniques improve the antiattack capability of the systems when used for secure communication.

scholarly journals Combination Synchronization of Fractional Systems Involving the Caputo–Hadamard Derivative

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2781
Author(s):  
Abdelhameed M. Nagy ◽  
Abdellatif Ben Makhlouf ◽  
Abdulaziz Alsenafi ◽  
Fares Alazemi
Keyword(s):  
Numerical Simulations ◽  
Fractional Order ◽  
Fractional Order Systems ◽  
Fractional Systems ◽  
Combination Synchronization ◽  
Response System ◽  
Drive Systems ◽  
Scaling Matrix ◽  
Hadamard Derivative ◽  
Theoretical Results

The main aim of this paper is to investigate the combination synchronization phenomena of various fractional-order systems using the scaling matrix. For this purpose, the combination synchronization is performed by considering two drive systems and one response system. We show that the combination synchronization phenomenon is achieved theoretically. Moreover, numerical simulations are carried out to confirm and validate the obtained theoretical results.

Multistability and Coexisting Attractors in a New Circulant Chaotic System

2019 ◽  
Vol 29 (13) ◽  
pp. 1950174 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Akif Akgul ◽  
Viet-Thanh Pham ◽  
Fawaz E. Alsaadi ◽  
Fahimeh Nazarimehr ◽  
...  
Keyword(s):  
Fractional Order ◽  
Order System ◽  
Cyclic Symmetry ◽  
Order Model ◽  
Coexisting Attractors ◽  
Circuit Realization ◽  
Chaotic Flow ◽  
Fractional Order Model ◽  
Dynamical Properties ◽  
Fractional Orders

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various fractional orders. Bifurcation analysis of the fractional order system shows that it has a kind of multistability like the integer order system, which is a very rare phenomenon. Circuit realization of the proposed system is also carried out to show that it is usable for engineering applications.

BIFURCATIONS AND CHAOS IN FRACTIONAL-ORDER SIMPLIFIED LORENZ SYSTEM

2010 ◽  
Vol 20 (04) ◽  
pp. 1209-1219 ◽  
Author(s):  
KEHUI SUN ◽  
XIA WANG ◽  
J. C. SPROTT
Keyword(s):  
Fractional Order ◽  
Lorenz System ◽  
Complex Dynamics ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Fractional Order Systems ◽  
Wide Range ◽  
The Time Domain ◽  
Fractional Orders ◽  
Simplified Lorenz System

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz system using the time-domain scheme. Chaos does exist in this system for a wide range of fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent. Both the system parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this system to yield chaos is 2.62.

scholarly journals Compound-combination synchronization of chaos in identical and different orders chaotic systems

2015 ◽  
Vol 25 (4) ◽  
pp. 463-490 ◽  
Author(s):  
K. S. Ojo ◽  
A. N. Njah ◽  
O. I. Olusola
Keyword(s):  
Chaotic Systems ◽  
Initial Conditions ◽  
Sufficient Conditions ◽  
Backstepping Technique ◽  
Third Order ◽  
Combination Synchronization ◽  
Response Systems ◽  
Drive Systems ◽  
Synchronization Scheme ◽  
Insight Into

Abstract This paper proposes a new synchronization scheme called compound-combination synchronization. The scheme is investigated using six chaotic Josephson junctions evolving from different initial conditions based on the drive-response configuration via the active backstepping technique. The technique is applied to achieve compound-combination synchronization of: (i) six identical third order resistive-capacitive-inductive-shunted Josepshon junctions (RCLSJJs) (with three as drive and three as response systems); (ii) three third order RCLSJJs (as drive systems) and three second order resistive-capacitive-shunted Josepshon junctions (RCSJJs (as response systems). In each case, sufficient conditions for global asymptotic stability for compound-combination synchronization to any desired scaling factors are achieved. Numerical simulations are employed to verify the feasibility and effectiveness of the compound-combination synchronization scheme. The result shows that this scheme could be used to vary the junction signal to any desired level and also give a better insight into synchronization in biological systems wherein different organs of different dynamical structures and orders are involved. The scheme could also provide high security in information transmission due to the complexity of its dynamical formulation.

scholarly journals Synchronization for a Class of Fractional-Order Hyperchaotic System and Its Application

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Wen Tan ◽  
Feng Ling Jiang ◽  
Chuang Xia Huang ◽  
Lan Zhou
Keyword(s):  
Theoretical Analysis ◽  
Fractional Order ◽  
Secure Communication ◽  
Controller Design ◽  
Design Method ◽  
Hyperchaotic System ◽  
Response System ◽  
Control Scheme ◽  
The Stability ◽  
Hyperchaotic Systems

A new controller design method is proposed to synchronize the fractional-order hyperchaotic system through the stability theory of fractional calculus; the synchronization between two identical fractional-order Chen hyperchaotic systems is realized by designing only two suitable controllers in the response system. Furthermore, this control scheme can be used in secure communication via the technology of chaotic masking using the complex nonperiodic information as trial message, and the useful information can be recovered at the receiver. Numerical simulations coincide with the theoretical analysis.

Fractional Hyperchaotic Telecommunication Systems: A New Paradigm

2013 ◽  
Vol 8 (3) ◽  
Author(s):  
Abolhassan Razminia ◽  
Dumitru Baleanu
Keyword(s):  
Fractional Order ◽  
Data Transmission ◽  
Secure Communication ◽  
Complex Dynamics ◽  
Order System ◽  
Fractional Order Systems ◽  
New Paradigm ◽  
Telecommunication System ◽  
Telecommunication Systems ◽  
Synchronization Scheme

The dynamics of hyperchaotic and fractional-order systems have increasing attracted attention in recent years. In this paper, we mix two complex dynamics to construct a new telecommunication system. Using a hyperchaotic fractional order system, we propose a novel synchronization scheme between receiver and transmitter which increases the security of data transmission and communication. Indeed, this is first work that can open a new way in secure communication system.

scholarly journals Parameter Identification and The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System Under Stochastic Disturbances

2021 ◽  
Author(s):  
Weiqiu Pan ◽  
Tianzeng Li ◽  
Yu Wang
Keyword(s):  
Fractional Order ◽  
Sliding Mode ◽  
Lyapunov Stability Theory ◽  
Control Technique ◽  
State Variables ◽  
Stochastic Disturbances ◽  
Unknown Parameters ◽  
Combination Synchronization ◽  
Special Cases ◽  
Drive Systems

Abstract This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part is divided into two cases, namely, the dimension of the drive-response system are different (or same). Firstly, a FO sliding surface was established in term of fractional calculus. Secondly, depended on the FO Lyapunov stability theory, the adaptive control technology and sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed, so that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed and the upper bound of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the demonstrated scheme via MATLAB.

Active Control for Multi-Switching Combination Synchronization of Non-Identical Chaotic Systems

2018 ◽  
pp. 129-162 ◽  
Author(s):  
Shikha Singh ◽  
Ahmad Taher Azar ◽  
Muzaffar Ahmad Bhat ◽  
Sundarapandian Vaidyanathan ◽  
Adel Ouannas
Keyword(s):  
Information Security ◽  
Numerical Simulations ◽  
Active Control ◽  
Chaotic Systems ◽  
Control Technique ◽  
Slave System ◽  
Combination Synchronization ◽  
Wide Range ◽  
Synchronization Scheme ◽  
Theoretical Results

This chapter investigates the multi-switching combination synchronization of three non-identical chaotic systems via active control technique. In recent years, some advances have been made with the idea of multi-switching combination synchronization. The different states of the master systems are synchronized with the desired state of the slave system in multi-switching combination synchronization scheme. The relevance of such kinds of synchronization studies to information security is evident in the wide range of possible synchronization directions that exist due to multi-switching synchronization. Numerical simulations justify the validity of the theoretical results discussed.

scholarly journals A New Type of Combination Synchronization among Multiple Chaotic Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Xingxu Wang ◽  
Lin Sun ◽  
Bingji Wang ◽  
Tousheng Huang
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Stability Theorem ◽  
Lyapunov Stability Theorem ◽  
Representative Case ◽  
Combination Synchronization ◽  
Response System ◽  
New Type ◽  
Drive Systems ◽  
Multiple Chaotic Systems

Based on former combination synchronization studies, a new type of combination synchronization approach is developed in this research, with the consideration of parallel combination of drive systems. This new synchronization approach is referred to as combination synchronization-II. As a representative case, the combination synchronization-II between three drive systems and one response system is studied. Applying Lyapunov stability theorem and active backstepping design, sufficient conditions for the proposed combination synchronization approach are derived. Numerical simulations are performed to show the feasibility and effectiveness of the proposed approach. Based on the investigation in this research, the proposed approach provides an applicable method for designing universal combination synchronization among multiple chaotic systems.

scholarly journals Generalized Dynamic Switched Synchronization between Combinations of Fractional-Order Chaotic Systems

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Wafaa S. Sayed ◽  
Moheb M. R. Henein ◽  
Salwa K. Abd-El-Hafiz ◽  
Ahmed G. Radwan
Keyword(s):  
Fractional Order ◽  
Secure Communication ◽  
Communication Systems ◽  
Chaotic Systems ◽  
Mathematical Formulation ◽  
Dynamic Scaling ◽  
Scaling Factors ◽  
Operating Modes ◽  
Master System ◽  
Synchronization Scheme

This paper proposes a novel generalized switched synchronization scheme amongnfractional-order chaotic systems with various operating modes. Digital dynamic switches and dynamic scaling factors are employed, which offer many new capabilities. Dynamic switches determine the role of each system as a master or a slave. A system can either have a fixed role throughout the simulation time (static switching) or switch its role one or more times (dynamic switching). Dynamic scaling factors are used for each state variable of the master system. Such scaling factors control whether the master is a single system or a combination of several systems. In addition, these factors determine the generalized relation between the original systems from which the master system is built as well as the slave system(s). Moreover, they can be utilized to achieve different kinds of generalized synchronization relations for the purpose of generating new attractor diagrams. The paper presents a mathematical formulation and analysis of the proposed synchronization scheme. Furthermore, many numerical simulations are provided to demonstrate the successful generalized switched synchronization of several fractional-order chaotic systems. The proposed scheme provides various functions suitable for applications such as different master-slave communication models and secure communication systems.

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