scholarly journals Determining the Lyapunov Spectrum of Continuous-Time 1D and 2D Multiscroll Chaotic Oscillators via the Solution ofm-PWL Variational Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jesus Manuel Munoz-Pacheco ◽  
Luz del Carmen Gómez-Pavón ◽  
Olga Guadalupe Félix-Beltrán ◽  
Arnulfo Luis-Ramos
Keyword(s):  
Lyapunov Exponents ◽  
Dynamic Range ◽  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
System Level ◽  
Design Parameters ◽  
Chaotic Oscillator ◽  
Chaotic Oscillators ◽  
Variational Equations ◽  
The Impact

An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on themregions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents fromm-piecewise linear variational equations and their associatedm-Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.

Design of a Robust Memristive Spiking Neuromorphic System with Unsupervised Learning in Hardware

2021 ◽  
Vol 17 (4) ◽  
pp. 1-26
Author(s):  
Md Musabbir Adnan ◽  
Sagarvarma Sayyaparaju ◽  
Samuel D. Brown ◽  
Mst Shamim Ara Shawkat ◽  
Catherine D. Schuman ◽  
...  
Keyword(s):  
Unsupervised Learning ◽  
Recognition Task ◽  
Single Layer ◽  
Process Variations ◽  
Spike Timing ◽  
System Level ◽  
Design Parameters ◽  
Digital Pulse ◽  
Neuromorphic System ◽  
The Impact

Spiking neural networks (SNN) offer a power efficient, biologically plausible learning paradigm by encoding information into spikes. The discovery of the memristor has accelerated the progress of spiking neuromorphic systems, as the intrinsic plasticity of the device makes it an ideal candidate to mimic a biological synapse. Despite providing a nanoscale form factor, non-volatility, and low-power operation, memristors suffer from device-level non-idealities, which impact system-level performance. To address these issues, this article presents a memristive crossbar-based neuromorphic system using unsupervised learning with twin-memristor synapses, fully digital pulse width modulated spike-timing-dependent plasticity, and homeostasis neurons. The implemented single-layer SNN was applied to a pattern-recognition task of classifying handwritten-digits. The performance of the system was analyzed by varying design parameters such as number of training epochs, neurons, and capacitors. Furthermore, the impact of memristor device non-idealities, such as device-switching mismatch, aging, failure, and process variations, were investigated and the resilience of the proposed system was demonstrated.

scholarly journals PVT-Robust CMOS Programmable Chaotic Oscillator: Synchronization of Two 7-Scroll Attractors

Electronics ◽  
2018 ◽  
Vol 7 (10) ◽  
pp. 252 ◽  
Author(s):  
Victor Carbajal-Gomez ◽  
Esteban Tlelo-Cuautle ◽  
Carlos Sanchez-Lopez ◽  
Francisco Fernandez-Fernandez
Keyword(s):  
Integrated Circuit ◽  
Secure Communication ◽  
Piecewise Linear ◽  
Cmos Technology ◽  
Oxide Semiconductor ◽  
Chaotic Attractors ◽  
Chaotic Oscillator ◽  
Maximum Lyapunov Exponent ◽  
Chaotic Oscillators ◽  
Cmos Integrated Circuit

Designing chaotic oscillators using complementary metal-oxide-semiconductor (CMOS) integrated circuit technology for generating multi-scroll attractors has been a challenge. That way, we introduce a current-mode piecewise-linear (PWL) function based on CMOS cells that allow programmable generation of 2–7-scroll chaotic attractors. The mathematical model of the chaotic oscillator designed herein has four coefficients and a PWL function, which can be varied to provide a high value of the maximum Lyapunov exponent. The coefficients are implemented electronically by designing operational transconductance amplifiers that allow programmability of their transconductances. Design simulations of the chaotic oscillator are provided for the 0.35 μ m CMOS technology. Post-layout and process–voltage–temperature (PVT) variation simulations demonstrate robustness of the multi-scroll chaotic attractors. Finally, we highlight the synchronization of two seven-scroll attractors in a master–slave topology by generalized Hamiltonian forms and observer approach. Simulation results show that the synchronized CMOS chaotic oscillators are robust to PVT variations and are suitable for chaotic secure communication applications.

Chaotic Oscillator Based on Fractional Order Memcapacitor

2019 ◽  
Vol 28 (14) ◽  
pp. 1950239 ◽  
Author(s):  
Akif Akgul
Keyword(s):  
Mathematical Model ◽  
Lyapunov Exponents ◽  
Fractional Order ◽  
Nonlinear Oscillator ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Chaotic Oscillator ◽  
State Equations ◽  
Chaotic Oscillators ◽  
Eigen Values

Many literatures have discussed fractional order memristor and memcapacitor-based chaotic oscillators but the entire oscillator model is considered to be of fractional order. My interest is to propose a nonlinear oscillator with considering only the memcapacitor element of fractional order. Hence, I propose a fractional order memcapacitor (FMC)-based novel chaotic oscillator. The complete mathematical model for the proposed oscillator is derived and presented in this paper. The dimensionless state equations are then analyzed by using the equilibrium points and their stability, Eigen values, Kaplan–Yorke dimensions and Lyapunov exponents. To understand the complete dynamical behavior, bifurcation graphs are obtained and presented. Finally, the proposed fractional memcapacitor oscillator is implemented by using the shelf components.

scholarly journals Automatic synthesis of 2D‐n‐scrolls chaotic systems by behavioral modeling

2009 ◽  
Vol 7 (01) ◽  
Author(s):  
J. M. Muñoz-Pacheco ◽  
E. Tlelo-Cuautle
Keyword(s):  
Chaotic Systems ◽  
Piecewise Linear ◽  
Electronic System ◽  
System Level ◽  
Operational Amplifiers ◽  
Piecewise Linear Approximation ◽  
Chaotic Oscillator ◽  
State Variables ◽  
Breaking Points ◽  
High Level

This paper introduces the guidelines to synthesize 2D chaotic systems by means of high‐level descriptions. The aim of this investigation is to synthesize 2D‐n‐scrolls chaotic systems based on saturated functions with multisegments. The new methodology of circuit synthesis is performed by three hierarchical levels. First, the 2D chaotic oscillator is numerically simulated at the electronic system level by applying state variables and piecewise‐linear approximation. Second, the excursion levels of the chaotic signals are scaled to control the breaking points and slopes of the saturated functions within practical values. Additionally, the frequency scaling of 2D‐n‐scrolls chaotic attractors is performed. Finally, current and voltage saturated functions are synthesized using Verilog‐A models for the operational amplifiers and in this manner a 2D chaotic system is synthesized using operational amplifiers to generate 2D‐n‐scrolls attractors. Numerical results are confirmed by H‐SPICE simulations to show the usefulness of the proposed synthesis approach.

Information Driven Product Development: A Framework for Product Design and Analysis Integration

2007 ◽  
Author(s):  
Angran Xiao
Keyword(s):  
Product Development ◽  
Product Information ◽  
Information Model ◽  
Product Lifecycle Management ◽  
System Level ◽  
Design Parameters ◽  
Analysis Model ◽  
Element Analysis ◽  
Product Information Model ◽  
The Impact

New paradigms and accompanying software systems are necessary to support the integration of system level design and discipline level analysis activities for the implementation of product lifecycle management. In this paper, we present an information driven product development method for the integration in the context of multidisciplinary product realization. The method contains three constituents: product information model which represents the associativities among design requirements, product components, and design parameters; compromise Decision Support Problem which maps the information model directly into design problems; and knowledge based Finite Element Analysis which generates analysis model automatically from the information model. Information driven product development uses product information model as a communication media between design and analysis activities, hence provides an effective way to trace the impact of design changes, facilitates the reuse of analyses models, and supports collaborative decision-making. An electronic chip package design and analysis scenario is presented to illustrate and demonstrate this method.

Comparative assessment of morphological mechanisms of maintaining structural liver homeostasis in the dynamics of exposure to coal-rock dust and sodium fluoride on the body

2020 ◽  
pp. 189-194
Author(s):  
M. S. Bugaeva ◽  
O. I. Bondarev ◽  
N. N. Mikhailova ◽  
L. G. Gorokhova
Keyword(s):  
Sodium Fluoride ◽  
Morphological Changes ◽  
The Body ◽  
System Level ◽  
Production Factor ◽  
Coal Rock ◽  
The Impact ◽  
Structural Homeostasis ◽  
Rock Dust

Introduction. The impact on the body of such factors of the production environment as coal-rock dust and fluorine compounds leads to certain shift s in strict indicators of homeostasis at the system level. Maintaining the relative constancy of the internal environment of the body is provided by the functional consistency of all organs and systems, the leading of which is the liver. Organ repair plays a crucial role in restoring the structure of genetic material and maintaining normal cell viability. When this mechanism is damaged, the compensatory capabilities of the organ are disrupted, homeostasis is disrupted at the cellular and organizational levels, and the development of the main pathological processes is noted.The aim of the study is to compare the morphological mechanisms of maintaining structural homeostasis of the liver in the dynamics of the impact on the body of coal-rock dust and sodium fluoride.Materials and methods. Experimental studies were conducted on adult white male laboratory rats. Features of morphological mechanisms for maintaining structural homeostasis of the liver in the dynamics of exposure to coal-rock dust and sodium fluoride were studied on experimental models of pneumoconiosis and fluoride intoxication. For histological examination in experimental animals, liver sampling was performed after 1, 3, 6, 9, 12 weeks of the experiment.Results. The specificity of morphological changes in the liver depending on the harmful production factor was revealed. It is shown that chronic exposure to coal-rock dust and sodium fluoride is characterized by the development of similar morphological changes in the liver and its vessels from the predominance of the initial compensatory-adaptive to pronounced violations of the stromal and parenchymal components. Long-term inhalation of coal-rock dust at 1–3 weeks of seeding triggers adaptive mechanisms in the liver in the form of increased functional activity of cells, formation of double-core hepatocytes, activation of immunocompetent cells and endotheliocytes, ensuring the preservation of the parenchyma and the general morphostructure of the organ until the 12th week of the experiment. Exposure to sodium fluoride leads to early disruption of liver compensatory mechanisms and the development of dystrophic changes in the parenchyma with the formation of necrosis foci as early as the 6th week of the experiment.Conclusions. The study of mechanisms for compensating the liver structure in conditions of long-term exposure to coal-rock dust and sodium fluoride, as well as processes that indicate their failure, and the timing of their occurrence, is of theoretical and practical importance for developing recommendations for the timely prevention and correction of pathological conditions developing in employees of the aluminum and coal industry.The authors declare no conflict of interests.

EFFECTS OF TREND AND PERIODICITY ON THE CORRELATION DIMENSION AND THE LYAPUNOV EXPONENTS

2008 ◽  
Vol 18 (12) ◽  
pp. 3679-3687 ◽  
Author(s):  
AYDIN A. CECEN ◽  
CAHIT ERKAL
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Lyapunov Exponents ◽  
Correlation Dimension ◽  
Time Series Data ◽  
Logistic Map ◽  
Model Identification ◽  
Series Data ◽  
Largest Lyapunov Exponent ◽  
The Impact

We present a critical remark on the pitfalls of calculating the correlation dimension and the largest Lyapunov exponent from time series data when trend and periodicity exist. We consider a special case where a time series Zi can be expressed as the sum of two subsystems so that Zi = Xi + Yi and at least one of the subsystems is deterministic. We show that if the trend and periodicity are not properly removed, correlation dimension and Lyapunov exponent estimations yield misleading results, which can severely compromise the results of diagnostic tests and model identification. We also establish an analytic relationship between the largest Lyapunov exponents of the subsystems and that of the whole system. In addition, the impact of a periodic parameter perturbation on the Lyapunov exponent for the logistic map and the Lorenz system is discussed.

scholarly journals How Many Inflections are There in the Lyapunov Spectrum?

2021 ◽  
Author(s):  
O. Jenkinson ◽  
M. Pollicott ◽  
P. Vytnova
Keyword(s):  
Piecewise Linear ◽  
Lyapunov Spectrum ◽  
Stat Phys ◽  
Linear Map ◽  
Piecewise Linear Map ◽  
Expanding Map ◽  
Lyapunov Spectra ◽  
Linear Maps ◽  
Inflection Points ◽  
Piecewise Linear Maps

AbstractIommi and Kiwi (J Stat Phys 135:535–546, 2009) showed that the Lyapunov spectrum of an expanding map need not be concave, and posed various problems concerning the possible number of inflection points. In this paper we answer a conjecture in Iommi and Kiwi (2009) by proving that the Lyapunov spectrum of a two branch piecewise linear map has at most two points of inflection. We then answer a question in Iommi and Kiwi (2009) by proving that there exist finite branch piecewise linear maps whose Lyapunov spectra have arbitrarily many points of inflection. This approach is used to exhibit a countable branch piecewise linear map whose Lyapunov spectrum has infinitely many points of inflection.

Making Up 3D Bodies

2021 ◽  
Vol 4 (2) ◽  
pp. 1-9
Author(s):  
Kiona Hagen Niehaus ◽  
Rebecca Fiebrink
Keyword(s):  
Software Tool ◽  
The Body ◽  
Design Parameters ◽  
Artistic Practice ◽  
Human Form ◽  
Modeling Systems ◽  
Exploratory Approach ◽  
Disability Status ◽  
High Level ◽  
The Impact

This paper describes the process of developing a software tool for digital artistic exploration of 3D human figures. Previously available software for modeling mesh-based 3D human figures restricts user output based on normative assumptions about the form that a body might take, particularly in terms of gender, race, and disability status, which are reinforced by ubiquitous use of range-limited sliders mapped to singular high-level design parameters. CreatorCustom, the software prototype created during this research, is designed to foreground an exploratory approach to modeling 3D human bodies, treating the digital body as a sculptural landscape rather than a presupposed form for rote technical representation. Building on prior research into serendipity in Human-Computer Interaction and 3D modeling systems for users at various levels of proficiency, among other areas, this research comprises two qualitative studies and investigation of the impact on the first author's artistic practice. Study 1 uses interviews and practice sessions to explore the practices of six queer artists working with the body and the language, materials, and actions they use in their practice; these then informed the design of the software tool. Study 2 investigates the usability, creativity support, and bodily implications of the software when used by thirteen artists in a workshop. These studies reveal the importance of exploration and unexpectedness in artistic practice, and a desire for experimental digital approaches to the human form.

scholarly journals Simulation Tests of a Cow Milking Machine—Analysis of Design Parameters

Processes ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 1358
Author(s):  
Ewa Golisz ◽  
Adam Kupczyk ◽  
Maria Majkowska ◽  
Jędrzej Trajer
Keyword(s):  
Mathematical Model ◽  
Simplified Model ◽  
Design Parameters ◽  
Degree Polynomial ◽  
Fourth Degree ◽  
Local Loss ◽  
Linear Drag ◽  
Milking Machine ◽  
Machine Analysis ◽  
The Impact

The objective of this paper was to create a mathematical model of vacuum drops in a form that enables the testing of the impact of design parameters of a milking cluster on the values of vacuum drops in the claw. Simulation tests of the milking cluster were conducted, with the use of a simplified model of vacuum drops in the form of a fourth-degree polynomial. Sensitivity analysis and a simulation of a model with a simplified structure of vacuum drops in the claw were carried out. As a result, the impact of the milking machine’s design parameters on the milking process could be analysed. The results showed that a change in the local loss and linear drag coefficient in the long milk duct will have a lower impact on vacuum drops if a smaller flux of inlet air, a higher head of the air/liquid mix, and a higher diameter of the long milk tube are used.

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