A chaotic jerk system with different types of equilibria and its application in communication system

In this paper, a new jerk system is designed. This system can display different characters of equilibrium points according to the value of its parameters. The proposed nonlinear oscillator can have both self-excited and hidden attractors. Dynamical properties of this system are investigated with the help of eigenvalues of equilibria, Lyapunov exponents' spectrum, and bifurcation diagrams. Also, an electronic circuit implementation is carried out to show the feasibility of this system. As an engineering application of this new chaotic jerk system, a chaotic communication system is realized by correlation delay shift keying. When the results of the communication system are examined, the transmitted information signal is successfully obtained in the receiving unit, and its performance efficiency is investigated in the presence of additive white Gaussian noise

A New 3-D Multistable Chaotic System with Line Equilibrium: Dynamic Analysis and Synchronization

This work introduces a new 3-D chaotic system with a line of equilibrium points. We carry out a detailed dynamic analysis of the proposed chaotic system with five nonlinear terms. We show that the chaotic system exhibits multistability with two coexisting chaotic attractors. We apply integral sliding mode control for the complete synchronization of the new chaotic system with itself as leader-follower systems

Temperature as a Chaotic Circuit Bifurcation Parameter

The number of researches aimed at understanding the chaotic behavior of nonlinear dynamical systems has grown considerably in recent years. The development of electronic circuits that exhibit this type of behavior has been the interest of numerous works in the literature. Among the possible sets of nonlinear systems, the simplest in which one can observe bifurcation phenomena and chaotic behavior, followed by well– controlled experiments, are nonlinear electronic circuits. One of the most widely used tools for analysis and evaluation of chaotic behavior is known as the bifurcation diagram. Generally, in the analysis of these circuits, parameters such as voltage, current and frequency are used to verify their respective behaviors. Variable values of passive components such as resistors and capacitors are also widely used. The temperature has also been used as a bifurcation parameter in resistor, diode and inductor (RLD) circuits. However, there is little attention from the scientific community on temperature as a bifurcation parameter for electronic circuits using operational amplifiers such as the chaotic Jerk circuit. In this sense, this project aims to implement a chaotic Jerk circuit, composed of operational amplifiers, resistors and capacitors, and subject it to different temperature levels, using this variable as an analysis parameter. Thus, at the end of this work it was possible to verify that the temperature variation directly influences the behavior of the investigated system, thus reaching the final objective of the project, presenting that the temperature can be a bifurcation parameter for a chaotic Jerk circuit

Desain dan Simulasi Numerik Sinkronisasi Unidirectional Sirkuit Jerk Serta Aplikasinya pada Sistem Keamanan Komunikasi

Sistem chaos mempunyai karakteristik unik yang nilainya sangat sensitif terhadap perubahan parameter dan kondisi awal, mirip dengan perilaku acak namun tetap deterministik. Chaos mempunyai potensi yang baik untuk dijadikan sistem keamanan komunikasi. Dalam makalah ini, kami menunjukkan  fenomena chaos dari sirkuit Jerk dengan modulus non-linier. Perilaku chaos ini berfungsi sebagai variabel parameter kontrol. Penelitian awal dalam makalah ini adalah menganalisis diagram fase, diagram bifurkasi dan peta Poincare dari sirkuit Jerk. Analisis sinkronisasi unidirectional antara dua sistem chaos yang identik juga telah disajikan dalam makalah ini. Berdasarkan hasil sinkronisasi chaos tersebut, akhirnya efektivitas sinkronisasi unidirectional antara dua sistem Jerk yang identik dalam sistem keamanan komunikasi menunjukkan potensi untuk dijadikan sebagai masking pengiriman data. Integrasi fisika teoritis, simulasi numerik menggunakan MATLAB serta implementasi simulasi sirkuit menggunakan MultiSIM telah dilakukan dalam makalah ini

Desain dan Simulasi Numerik Sinkronisasi Unidirectional Sirkuit Jerk Serta Aplikasinya pada Sistem Keamanan Komunikasi

Sistem chaos mempunyai karakteristik unik yang nilainya sangat sensitif terhadap perubahan parameter dan kondisi awal, mirip dengan perilaku acak namun tetap deterministik. Chaos mempunyai potensi yang baik untuk dijadikan sistem keamanan komunikasi. Dalam makalah ini, kami menunjukkan  fenomena chaos dari sirkuit Jerk dengan modulus non-linier. Perilaku chaos ini berfungsi sebagai variabel parameter kontrol. Penelitian awal dalam makalah ini adalah menganalisis diagram fase, diagram bifurkasi dan peta Poincare dari sirkuit Jerk. Analisis sinkronisasi unidirectional antara dua sistem chaos yang identik juga telah disajikan dalam makalah ini. Berdasarkan hasil sinkronisasi chaos tersebut, akhirnya efektivitas sinkronisasi unidirectional antara dua sistem Jerk yang identik dalam sistem keamanan komunikasi menunjukkan potensi untuk dijadikan sebagai masking pengiriman data. Integrasi fisika teoritis, simulasi numerik menggunakan MATLAB serta implementasi simulasi sirkuit menggunakan MultiSIM telah dilakukan dalam makalah ini

DESAIN DAN SIMULASI NUMERIK SINKRONISASI UNIDIRECTIONAL SIRKUIT JERK DAN APLIKASINYA UNTUK SISTEM KEAMANAN KOMUNIKASI

Sistem chaos mempunyai karakteristik ketergantungan yang sensitif pada kondisi awal, mirip dengan perilaku acak, dan memiliki strange attractor yang unik. Chaos mempunyai potensi yang baik untuk dijadikan sistem keamanan komunikasi. Dalam makalah ini, kami menunjukkan beberapa fenomena yang menarik dari tiga orde sirkuit Jerk dengan modulus non-linier. Perilaku chaos ini berfungsi sebagai variabel parameter kontrol. Penelitian awal dalam makalah ini adalah menganalisis diagram fase, diagram bifurkasi dan peta Poincare. Analisis sinkronisasi dalam kasus sinkronisasi unidirectional antara dua sistem chaos yang identik juga telah disajikan. Berdasarkan hasil sinkronisasi chaos tersebut, akhirnya efektivitas skema sinkronisasi unidirectional antara dua sistem Jerk yang identik dalam sistem keamanan komunikasi disajikan secara rinci dan menunjukkan potensi untuk dijadikan sebagai masking data. Integrasi fisika teoritis, simulasi numerik dengan menggunakan MATLAB serta implementasi simulasi sirkuit dengan menggunakan MultiSIM telah dilakukan dalam makalah ini

Rikitake dynamo system, its circuit simulation and chaotic synchronization via quasi-sliding mode control

Rikitake dynamo system (1958) is a famous two-disk dynamo model that is capable of executing nonlinear chaotic oscillations similar to the chaotic oscillations as revealed by palaeomagnetic study. First, we detail the Rikitake dynamo system, its signal plots and important dynamic properties. Then a circuit design using Multisim is carried out for the Rikitake dynamo system. New synchronous quasi-sliding mode control (QSMC) for Rikitake chaotic system is studied in this paper. Furthermore, the selection on switching surface and the existence of QSMC scheme is also designed in this paper. The efficiency of the QSMC scheme is illustrated with MATLAB plots

Análisis, construcción, simulación y sincronización de circuitos electrónicos prototipos de Caos

El proyecto tiene como objetivo el estudio de siete Sistemas Dinámicos, yendo de los que son paradigma de Caos a los más complejos, y sus posibles aplicaciones en comunicaciones privadas, bioingeniería y comunicaciones ópticas. El conjunto de sistemas seleccionados incluye algunos ejemplos paradigmáticos de Dinámicas Caóticas, así como nuevas propuestas, tanto de do sistemas básicos como de un sistema que tiene soluciones más complejas, nunca antes estudiados. Se logrará, de esta manera, realizar un completo recorrido desde los osciladores no-lineales más simples (como el de Van Der Pol), hasta los sistemas de mayor complejidad (como son las dinámicas hipercaóticas). El estudio consiste, en primer lugar, en identificar los métodos de análisis específicos del Caos, que permiten poner de manifiesto su carácter y propiedades (a lo que se dedicará el capítulo 1). Tras ello (Capítulo 2 y 3), se desarrollan, estudian y analizan los sistemas mediante simulaciones numéricas de la dinámica de los citados sistemas utilizando el software matemático MATLAB. En una segunda parte (que abarca la primera mitad del Capítulo 4), se implementan los circuitos electrónicos de los citados sistemas, y se simula su comportamiento mediante un software profesional. En una tercera parte (coincidente con la segunda mitad del Capítulo 4 y el Capítulo 5 completo), se construyen físicamente los sistemas fundamentales y sus extensiones, con el objetivo de caracterizar su comportamiento. Además, se desarrolla una aplicación software con entorno gráfico para el análisis sistemático de las dinámicas objeto de estudio. Finalmente, y con el objetivo de aplicar los Sistemas Dinámicos caóticos tanto a Comunicaciones Seguras como a Bioingeniería, este proyecto presenta un estudio de los citados sistemas para su uso en Comunicaciones Seguras, en el capítulo 6. Por otro lado, el oscilador de Van Der Pol no sólo es un sistema paradigma de Caos por la riqueza de su dinámica caótica, sino también por su interés en la simulación del corazón humano tanto en régimen regular, como en régimen caótico. Este análisis se desarrolla en el Capítulo 3

Low Power IoT based Automated Manhole Cover Monitoring System as a Smart City application

With the increased population in the big cities, Internet of Things (IoT) devices to be used as automated monitoring systems are required in many of the Smart city’s applications. Monitoring road infrastructure such as a manhole cover (MC) is one of these applications. Automating monitoring manhole cover structure has become more demanding, especially when the number of MC failure increases rapidly: it affects the safety, security and the economy of the society. Only 30% of the current MC monitoring systems are automated with short lifetime in comparison to the lifetime of the MC, without monitoring all the MC issues and without discussing the challenges of the design from IoT device design point of view. Extending the lifetime of a fully automated IoT-based MC monitoring system from circuit design point of view was studied and addressed in this research. The main circuit that consumes more power in the IoT-based MC monitoring system is the analogue to digital converter (ADC) found at the data acquisition module (DAQ). In several applications, the compressive sensing (CS) technique proved its capability to reduce the power consumption for ADC. In this research, CS has been investigated and studied deeply to reach the aim of the research. CS based ADC is named analogue to information converter (AIC). Because the heart of the AIC is the pseudorandom number generator (PRNG), several researchers have used it as a key to secure the data, which makes AIC more suitable for IoT device design. Most of these PRNG designs for AIC are hardware implemented in the digital circuit design. The presence of digital PRNG at the AIC analogue front end requires: a) isolating digital and analogue parts, and b) using two different power supplies and grounds for analogue and digital parts. On the other hand, analogue circuit design becomes more demanding for the sake of the power consumption, especially after merging the analogue circuit design with other fields such as neural networks and neuroscience. This has motivated the researcher to propose two low-power analogue chaotic oscillators to replace digital PRNG using opamp Schmitt Trigger. The proposed systems are based on a coupling oscillator concept. The design of the proposed systems is based on: First, two new modifications for the well-known astable multivibrator using opamp Schmitt trigger. Second, the waveshaping design technique is presented to design analogue chaotic oscillators instead of starting with complex differential equations as it is the case for most of the chaotic oscillator designs. This technique helps to find easy steps and understanding of building analogue chaotic oscillators for electronic circuit designers. The proposed systems used off the shelf components as a proof of concept. The proposed systems were validated based on: a) the range of the temperature found beneath a manhole cover, and b) the signal reconstruction under the presence and the absence of noise. The results show decent performance of the proposed system from the power consumption point of view, as it can exceed the lifetime of similar two opamps based Jerk chaotic oscillators by almost one year for long lifetime applications such as monitoring MC using Li-Ion battery. Furthermore, in comparison to PRNG output sequence generated by a software algorithm used in AIC framework in the presence of the noise, the first proposed system output sequence improved the signal reconstruction by 6.94%, while the second system improved the signal reconstruction by 17.83