Experimental Analysis of Emergent Dynamics in Complex Networks of Nonlinear Oscillators

The aim of this thesis is to explore and investigate the emergent dynamics of complex networks through a novel and insightful experimental setup realized as a configurable network of chaotic Chua's circuits. In particular part of our work has been devoted to the implementation and characterization of a "2.0 hardware version" of it, where the interconnection network has improved greatly in its main features. In this way the setup has been fully automatized in providing control on network structure and coupling strength. A large set of experiments has been carried out in networks with proportional coupling and arbitrary topology, showing, emergent dynamics encompassing synchronization, patterns and traveling waves, clusters formation. Also, the case of dynamic coupling has been experimentally addressed. The experimental observations have been compared with theoretical results by carrying out a local stability analysis of networks with static and dynamic links. Here we use the Master Stability approach (MSF) and its extensions to the case where the links are of dynamic nature (Proportional Derivative-MSF). Last part of the work has been devoted to the experimental study of cluster synchronization, stimulated by novel theoretical advances based on group theory and network symmetries. A novel network structure referred as "Multiplexed Network" has been experimentally examined, resulting in a great enhancement in synchronization, for which no theoretical models are yet available

Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.Comment: submitted to EP

Field-programmable gate array design of image encryption and decryption using Chua’s chaotic masking

This article presents a simple and efficient masking technique based on Chua chaotic system synchronization. It includes feeding the masked signal back to the master system and using it to drive the slave system for synchronization purposes. The proposed system is implemented in a field programmable gate array (FPGA) device using the Xilinx system generator tool. To achieve synchronization, the Pecora-Carroll identical cascading synchronization approach was used. The transmitted signal should be mixed or masked with a chaotic carrier and can be processed by the receiver without any distortion or loss. For different images, the security analysis is performed using the histogram, correlation coefficient, and entropy. In addition, FPGA hardware co-simulation based Xilinx Artix7 xc7a100t-1csg324 was used to check the reality of the encryption and decryption of the images

CMOS design of chaotic oscillators using state variables: a monolithic Chua's circuit

This paper presents design considerations for monolithic implementation of piecewise-linear (PWL) dynamic systems in CMOS technology. Starting from a review of available CMOS circuit primitives and their respective merits and drawbacks, the paper proposes a synthesis approach for PWL dynamic systems, based on state-variable methods, and identifies the associated analog operators. The GmC approach, combining quasi-linear VCCS's, PWL VCCS's, and capacitors is then explored regarding the implementation of these operators. CMOS basic building blocks for the realization of the quasi-linear VCCS's and PWL VCCS's are presented and applied to design a Chua's circuit IC. The influence of GmC parasitics on the performance of dynamic PWL systems is illustrated through this example. Measured chaotic attractors from a Chua's circuit prototype are given. The prototype has been fabricated in a 2.4- mu m double-poly n-well CMOS technology, and occupies 0.35 mm/sup 2/, with a power consumption of 1.6 mW for a +or-2.5-V symmetric supply. Measurements show bifurcation toward a double-scroll Chua's attractor by changing a bias current

Chaos via a piecewise-linear switch ed-capacitor circuit

A nonlinear switched-capacitor circuit that generates chaotic signals is reported. The circuit is described by a first-order piecewise-linear discrete equation that exhibits a chaotic dynamics. Experimental results illustrating the circuit performance and its use as a noise generator are included.Comisión Interministerial de Ciencia y Tecnología 3467-8

Secure transmission of information by digital chaotic signals

Protecting signals is one of the main tasks in information transmission. A large number of different methods have been employed since many centuries ago. Most of them have been based on the use of certain signal added to the original one. When the composed signal is received, if the added signal is known, the initial information may be obtained. The main problem is the type of masking signal employed. One possibility is the use of chaotic signals, but they have a first strong limitation: the need to synchronize emitter and receiver. Optical communications systems, based on chaotic signals, have been proposed in a large number of papers. Moreover, because most of the communication systems are digital and conventional chaos generators are analogue, a conversion analogue-digital is needed. In this paper we will report a new system where the digital chaos is obtained from an optically programmable logic structure. This structure has been employed by the authors in optical computing and some previous results in chaotic signals have been reported. The main advantage of this new system is that an analogue-digital conversion is not needed. Previous works by the authors employed Self-Electrooptical Effect Devices but in this case more conventional structures, as semiconductor laser amplifiers, have been employed. The way to analyze the characteristics of digital chaotic signals will be reported as well as the method to synchronize the chaos generators located in the emitter and in the receiver

Alternative memristor-based interconnect topologies for fast adaptive synchronization of chaotic circuits

© 2020 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/Resistive switching devices (memristors) constitute an emerging device technology promising for a vari- ety of applications that are currently being studied. In this context, the use of memristors as coupling el- ements of the dynamics of chaotic circuits for adaptive synchronization purposes, was recently proposed and the passive crossbar array was evaluated as target interconnect medium. Nonetheless, memristors may suffer from defects and degradation. Therefore, this work evaluates the impact of memristor switch- ing faults in an adaptive chaotic synchronization scheme, exploring at the same time the fault-tolerance of the crossbar architecture. Moreover, inspired from our observations in the stuck-at-OFF fault analy- sis of the memristive crossbar, some alternative scalable memristive interconnect patterns are suggested, whose performance is found independent of the number of interconnected chaotic circuits, requiring a much smaller number of total memristors than the crossbar array. All simulations are based on an ac- curate physics-based model of a bipolar memristor with filamentary switching mechanism. Based on our results, using the alternative topologies instead of the crossbar array leads to significant savings in the synchronization time that increase with the number of interconnected chaotic units, at the cost of more limited scaling capability and fault-tolerance.This work was supported in part by the Chilean research Grants ANID REDES ETAPA INICIAL 2017 No. REDI170604, ANID FONDECYT INICIACION 11180706, ANID BASAL FB0008, and by the Spanish MINECO and ERDF under Grant TEC2016-75151-C3-2-R.Peer ReviewedPostprint (author's final draft

New artificial neural network design for Chua chaotic system prediction using FPGA hardware co-simulation

This study aims to design a new architecture of the artificial neural networks (ANNs) using the Xilinx system generator (XSG) and its hardware co-simulation equivalent model using field programmable gate array (FPGA) to predict the behavior of Chua’s chaotic system and use it in hiding information. The work proposed consists of two main sections. In the first section, MATLAB R2016a was used to build a 3×4×3 feed forward neural network (FFNN). The training results demonstrate that FFNN training in the Bayesian regulation algorithm is sufficiently accurate to directly implement. The second section demonstrates the hardware implementation of the network with the XSG on the Xilinx artix7 xc7a100t-1csg324 chip. Finally, the message was first encrypted using a dynamic Chua system and then decrypted using ANN’s chaotic dynamics. ANN models were developed to implement hardware in the FPGA system using the IEEE 754 Single precision floating-point format. The ANN design method illustrated can be extended to other chaotic systems in general