A MULTIVIBRATOR CIRCUIT BASED ON CHAOS GENERATION

2012 ◽  
Vol 22 (01) ◽  
pp. 1250011 ◽  
Author(s):  
E. CAMPOS-CANTÓN ◽  
R. FEMAT ◽  
J. G. BARAJAS-RAMÍREZ ◽  
I. CAMPOS-CANTÓN
Keyword(s):  
Chaotic Systems ◽  
Pulse Generator ◽  
Piecewise Linear ◽  
Equilibrium Stability ◽  
Flip Flop ◽  
Chua’S Oscillator ◽  
Potential Applications ◽  
Bistable Potential ◽  
Linear Subsystem ◽  
Parametric Modulation

We present a parameterized method to design multivibrator circuits via piecewise-linear (PWL) chaotic systems, which can exhibit double-scroll oscillations. The circuit is conformed exploiting a parametric modulation that manipulates the equilibrium stability of each linear subsystem. Chua's oscillator is used as benchmark to illustrate the effectiveness of the proposed method to design multivibrator circuits. Thus, our proposal allows the design of the three configurations of a multivibrator: monostable, astable, and bistable. Potential applications are illustrated designing a pulse generator and a full S-R flip flop device based on our all-in-one multivibrator circuit.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS

1994 ◽  
Vol 04 (04) ◽  
pp. 979-998 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Chaotic Systems ◽  
Main Tool ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Unified Framework ◽  
Partial Synchronization ◽  
Chua’S Oscillator ◽  
And Control

In this paper, we give a framework for synchronization of dynamical systems which unifies many results in synchronization and control of dynamical systems, in particular chaotic systems. We define concepts such as asymptotical synchronization, partial synchronization and synchronization error bounds. We show how asymptotical synchronization is related to asymptotical stability. The main tool we use to prove asymptotical stability and synchronization is Lyapunov stability theory. We illustrate how many previous results on synchronization and control of chaotic systems can be derived from this framework. We will also give a characterization of robustness of synchronization and show that master-slave asymptotical synchronization in Chua’s oscillator is robust.

Noninvertible Piecewise Linear Maps Applied to Chaos Synchronization and Secure Communications

1997 ◽  
Vol 07 (07) ◽  
pp. 1617-1634 ◽  
Author(s):  
G. Millerioux ◽  
C. Mira
Keyword(s):  
Dynamical Systems ◽  
Chaos Synchronization ◽  
Chaotic Systems ◽  
Piecewise Linear ◽  
A Priori ◽  
Secure Communications ◽  
Technological Parameters ◽  
Linear Maps ◽  
Piecewise Linear Maps ◽  
Necessary And Sufficient

Recently, it was demonstrated that two chaotic dynamical systems can synchronize each other, leading to interesting applications as secure communications. We propose in this paper a special class of dynamical systems, noninvertible discrete piecewise linear, emphasizing on interesting advantages they present compared with continuous and differentiable nonlinear ones. The generic aspect of such systems, the simplicity of numerical implementation, and the robustness to mismatch of technological parameters make them good candidates. The classical concept of controllability in the control theory is presented and used in order to choose and predict the number of appropriate variables to be transmitted for synchronization. A necessary and sufficient condition of chaotic synchronization is established without computing numerical quantities, introducing a state affinity structure of chaotic systems which provides an a priori establishment of synchronization.

Implementation of MHLFF based low power pulse triggered flip flop

2017 ◽  
Vol 7 (1.1) ◽  
pp. 483
Author(s):  
Shreya Verma ◽  
Tunikipati Usharani ◽  
S Iswariya ◽  
Bhavana Godavarthi
Keyword(s):  
Low Power ◽  
Pulse Generator ◽  
Research Paper ◽  
Flip Flop ◽  
Power Pulse

The present research paper proposes to implement a low power pulse-triggered flip-flop. The proposed design is MHLFF (modified hybrid latch flip-flop). In MHLFF method, the pulse generator will be altered concerning illustration inverters what’s more a pasquinade transistor. This technique will be comparative should understood kind about flip flop what’s more it utilizes a static lock structure. Should succeed Most exceedingly bad situation delay issue brought on Eventually Tom's perusing discharging way comprise from claiming three stacked transistor MHLFF may be presented.  We can minimize the power and delay when compared to the existing models i.e, CDFF and SCDFF. The circuit was implementing using Cadence Virtuoso tool in 90-nm and 45-nm technology.

scholarly journals Multistable Systems with Hidden and Self-Excited Scroll Attractors Generated via Piecewise Linear Systems

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
R. J. Escalante-González ◽  
Eric Campos
Keyword(s):  
Vector Field ◽  
Linear Systems ◽  
Piecewise Linear ◽  
Hidden Attractor ◽  
Hidden Attractors ◽  
Key Space ◽  
Potential Applications ◽  
Current Design ◽  
Multistable Systems ◽  
Number Of Equilibria

In this work, we present an approach to design a multistable system with one-directional (1D), two-directional (2D), and three-directional (3D) hidden multiscroll attractor by defining a vector field on ℝ3 with an even number of equilibria. The design of multistable systems with hidden attractors remains a challenging task. Current design approaches are not as flexible as those that focus on self-excited attractors. To facilitate a design of hidden multiscroll attractors, we propose an approach that is based on the existence of self-excited double-scroll attractors and switching surfaces whose relationship with the local manifolds associated to the equilibria lead to the appearance of the hidden attractor. The multistable systems produced by the approach could be explored for potential applications in cryptography, since the number of attractors can be increased by design in multiple directions while preserving the hidden attractor allowing a bigger key space.

EXPERIMENTAL RESULTS ON CHUA'S CIRCUIT ROBUST SYNCHRONIZATION VIA LMIs

2007 ◽  
Vol 17 (09) ◽  
pp. 3199-3209 ◽  
Author(s):  
C. D. CAMPOS ◽  
R. M. PALHARES ◽  
E. M. A. M. MENDES ◽  
L. A. B. TORRES ◽  
L. A. MOZELLI
Keyword(s):  
Discrete Time ◽  
Chaotic Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Chua’S Oscillator ◽  
Laboratory Setup ◽  
Robust Synchronization ◽  
Discrete Time Systems ◽  
Main Ideas ◽  
Time Systems

This paper investigates the synchronization of coupled chaotic systems using techniques from the theory of robust [Formula: see text] control based on Linear Matrix Inequalities. To deal with the synchronization of a class of Lur'e discrete time systems, a project methodology is proposed. A laboratory setup based on Chua's oscillator circuit is used to demonstrate the main ideas of the paper in the context of the problem of information transmission.

Separation and synchronization of piecewise linear chaotic systems

2006 ◽  
Vol 74 (2) ◽  
Author(s):  
Paolo Arena ◽  
Arturo Buscarino ◽  
Luigi Fortuna ◽  
Mattia Frasca
Keyword(s):  
Chaotic Systems ◽  
Piecewise Linear

scholarly journals GENERATING MULTISCROLL CHAOTIC ATTRACTORS: THEORIES, METHODS AND APPLICATIONS

2006 ◽  
Vol 16 (04) ◽  
pp. 775-858 ◽  
Author(s):  
JINHU LÜ ◽  
GUANRONG CHEN
Keyword(s):  
Piecewise Linear ◽  
Rapid Development ◽  
Linear Functions ◽  
Future Research ◽  
Chaotic Attractors ◽  
Circuit Implementation ◽  
Practical Applications ◽  
Component Design ◽  
Potential Applications ◽  
Circuit Component

Over the last two decades, theoretical design and circuit implementation of various chaos generators have been a focal subject of increasing interest due to their promising applications in various real-world chaos-based technologies and information systems. In particular, generating complex multiscroll chaotic attractors via simple electronic circuits has seen rapid development. This article offers an overview of the subject on multiscroll chaotic attractors generation, including some fundamental theories, design methodologies, circuit implementations and practical applications. More precisely, the article first describes some effective design methods using piecewise-linear functions, cellular neural networks, nonlinear modulating functions, circuit component design, switching manifolds, multifolded tori formation, and so on. Based on different approaches, computer simulation and circuit implementation of various multiscroll chaotic attractors are then discussed in detail, with some theoretical proofs and laboratory experiments presented for verification and demonstration. It is then followed by some discussion on potential applications of multiscroll chaotic attractors, including secure and digital communications, synchronous prediction, random bit generation, and so on. The article is finally concluded with some future research outlooks, putting the important subject into engineering perspective.

FOLLOWING A SADDLE-NODE OF PERIODIC ORBITS' BIFURCATION CURVE IN CHUA'S CIRCUIT

2009 ◽  
Vol 19 (02) ◽  
pp. 487-495 ◽  
Author(s):  
E. FREIRE ◽  
E. PONCE ◽  
J. ROS
Keyword(s):  
Periodic Orbits ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Numerical Continuation ◽  
Bifurcation Curve ◽  
Saddle Node Bifurcation ◽  
Leading Role ◽  
Chua’S Oscillator ◽  
Saddle Node ◽  
Parametric Region

Starting from previous analytical results assuring the existence of a saddle-node bifurcation curve of periodic orbits for continuous piecewise linear systems, numerical continuation is done to get some primary bifurcation curves for the piecewise linear Chua's oscillator in certain dimensionless parameter plane. The primary period doubling, homoclinic and saddle-node of periodic orbits' bifurcation curves are computed. A Belyakov point is detected in organizing the connection of these curves. In the parametric region between period-doubling, focus-center-limit cycle and homoclinic bifurcation curves, chaotic attractors coexist with stable nontrivial equilibria. The primary saddle-node bifurcation curve plays a leading role in this coexistence phenomenon.

scholarly journals Generation Method of Multipiecewise Linear Chaotic Systems Based on the Heteroclinic Shil’nikov Theorem and Switching Control

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Chunyan Han ◽  
Fang Yuan ◽  
Xiaoyuan Wang
Keyword(s):  
Linear Systems ◽  
Circuit Design ◽  
Chaotic System ◽  
Chaotic Systems ◽  
Piecewise Linear ◽  
Equilibrium Points ◽  
Switching Control ◽  
Heteroclinic Loop ◽  
Dynamical Characteristics ◽  
Fundamental Systems

Based on the heteroclinic Shil’nikov theorem and switching control, a kind of multipiecewise linear chaotic system is constructed in this paper. Firstly, two fundamental linear systems are constructed via linearization of a chaotic system at its two equilibrium points. Secondly, a two-piecewise linear chaotic system which satisfies the Shil’nikov theorem is generated by constructing heteroclinic loop between equilibrium points of the two fundamental systems by switching control. Finally, another multipiecewise linear chaotic system that also satisfies the Shil’nikov theorem is obtained via alternate translation of the two fundamental linear systems and heteroclinic loop construction of adjacent equilibria for the multipiecewise linear system. Some basic dynamical characteristics, including divergence, Lyapunov exponents, and bifurcation diagrams of the constructed systems, are analyzed. Meanwhile, computer simulation and circuit design are used for the proposed chaotic systems, and they are demonstrated to be effective for the method of chaos anticontrol.

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