scholarly journals A novel family of 1-D robust chaotic maps

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dhrubajyoti Mandal
Keyword(s):  
Mathematical Models ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Infinite Family ◽  
Practical Applications ◽  
Smooth Maps ◽  
Wide Range ◽  
Chaotic Signals ◽  
Piecewise Smooth Maps ◽  
Parameter Values

AbstractChaotic dynamics of various continuous and discrete-time mathematical models are used frequently in many practical applications. Many of these applications demand the chaotic behavior of the model to be robust. Therefore, it has been always a challenge to find mathematical models which exhibit robust chaotic dynamics. In the existing literature there exist a very few studies of robust chaos generators based on simple 1-D mathematical models. In this paper, we have proposed an infinite family consisting of simple one-dimensional piecewise smooth maps which can be effectively used to generate robust chaotic signals over a wide range of the parameter values.

BORDER COLLISION BIFURCATIONS IN THREE-DIMENSIONAL PIECEWISE SMOOTH SYSTEMS

2008 ◽  
Vol 18 (02) ◽  
pp. 577-586 ◽  
Author(s):  
INDRAVA ROY ◽  
A. R. ROY
Keyword(s):  
Three Dimensional ◽  
Piecewise Smooth ◽  
Smooth Maps ◽  
Research Fields ◽  
Border Collision Bifurcations ◽  
Period 2 ◽  
Wide Range ◽  
Different Types ◽  
Piecewise Smooth Maps ◽  
The Stability

Piecewise smooth maps have been a focus of study for scientists in a wide range of research fields. These maps show qualitatively different types of bifurcations than those exhibited by generic smooth maps. We present a theoretical framework for analyzing three-dimensional piecewise smooth maps by deriving a suitable normal form and then finding the stability criteria for periodic orbits. We also show by numerical simulation different types of border collision bifurcations that can occur in such a map. We have also been able to observe a border collision bifurcation from a period-2 to a quasiperiodic orbit.

CONSTANT-PHASE-INDUCED CONTROL OF CHAOTIC CHARGED PARTICLES IN THE FIELD OF A WAVE PACKET

2013 ◽  
Vol 23 (06) ◽  
pp. 1330022
Author(s):  
RICARDO CHACÓN
Keyword(s):  
Charged Particle ◽  
Wave Packet ◽  
Finite Number ◽  
Lyapunov Exponents ◽  
Chaotic Dynamics ◽  
Chaotic Behavior ◽  
Charged Particles ◽  
Melnikov Method ◽  
Wide Range ◽  
Range Of Values

It is shown that the dissipative chaotic dynamics of a charged particle in the field of a wave packet with an arbitrary but finite number of harmonics can be reliably suppressed by judiciously varying the constant phase of the main harmonic, ϕ0, while keeping null the corresponding constant phases of the remaining harmonics. The dependence of the chaotic threshold on the wave packet parameters is predicted theoretically (Melnikov method) and confirmed numerically (Lyapunov exponents). In particular, it is shown that ϕ0 is effective at suppressing the chaotic behavior existing when ϕ0 = 0 over a wide range of values of the wave packet width, while the remaining parameters are kept constant.

Parameter Matching Using Adaptive Synchronization of Two Chua's Oscillators

2014 ◽  
Vol 24 (11) ◽  
pp. 1430032 ◽  
Author(s):  
Valentin Siderskiy ◽  
Vikram Kapila
Keyword(s):  
Adaptive Synchronization ◽  
Current Feedback ◽  
Control Laws ◽  
Adaptive Controllers ◽  
Wide Range ◽  
Chaotic Signals ◽  
Parameter Matching ◽  
And Performance ◽  
Set Up ◽  
Parameter Values

In this paper, we develop a parameter matching technique using adaptive synchronization with a chaotic attractor. Two Chua's oscillators, identical in every parameter except for one, are set-up in a master/slave configuration where the slave's mismatched parameter is adaptable. Using Lyapunov functions and incorporating the presence of chaotic signals, adaptive control laws are designed to ensure exact parameter matching. One of the derived adaptive controllers is experimentally validated by using an adaptive inductor-gyrator composed of current feedback op-amps (CFOAs). The experimental results are compared to high-fidelity SPICE simulations, and performance of adaptive controllers are compared over a wide range of parameter values using MATLAB.

Codimension-2 Border Collision, Bifurcations in One-Dimensional, Discontinuous Piecewise Smooth Maps

2014 ◽  
Vol 24 (02) ◽  
pp. 1450024 ◽  
Author(s):  
Laura Gardini ◽  
Viktor Avrutin ◽  
Irina Sushko
Keyword(s):  
Discontinuity Point ◽  
Piecewise Smooth ◽  
One Dimensional ◽  
Smooth Maps ◽  
Border Collision Bifurcations ◽  
Piecewise Smooth Maps ◽  
Symbolic Sequences ◽  
Bifurcation Structures ◽  
Local Monotonicity ◽  
Parameter Values

We consider a two-parametric family of one-dimensional piecewise smooth maps with one discontinuity point. The bifurcation structures in a parameter plane of the map are investigated, related to codimension-2 bifurcation points defined by the intersections of two border collision bifurcation curves. We describe the case of the collision of two stable cycles of any period and any symbolic sequences. For this case, we prove that the local monotonicity of the functions constituting the first return map defined in a neighborhood of the border point at the parameter values related to the codimension-2 bifurcation point determines, under suitable conditions, the kind of bifurcation structure originating from this point; this can be either a period adding structure, or a period incrementing structure, or simply associated with the coupling of colliding cycles.

A New Detector System For The HB5 Stem Instrument

1985 ◽  
Vol 43 ◽  
pp. 134-135
Author(s):  
J.M. Cowley
Keyword(s):  
Dark Field ◽  
Detector System ◽  
Electron Holography ◽  
Small Specimen ◽  
Bright Field ◽  
Multiple Images ◽  
Practical Applications ◽  
Wide Range ◽  
Diffraction Patterns ◽  
Operational Modes

The HB5 STEM instrument at ASU has been modified previously to include an efficient two-dimensional detector incorporating an optical analyser device and also a digital system for the recording of multiple images. The detector system was built to explore a wide range of possibilities including in-line electron holography, the observation and recording of diffraction patterns from very small specimen regions (having diameters as small as 3Å) and the formation of both bright field and dark field images by detection of various portions of the diffraction pattern. Experience in the use of this system has shown that sane of its capabilities are unique and valuable. For other purposes it appears that, while the principles of the operational modes may be verified, the practical applications are limited by the details of the initial design.

scholarly journals The simulation model for a flood management by flood control facilities

2018 ◽  
Vol 245 ◽  
pp. 15002 ◽  
Author(s):  
Roman Davydov ◽  
Valery Antonov ◽  
Dmitry Molodtsov ◽  
Alexey Cheremisin ◽  
Vadim Korablev
Keyword(s):  
Mathematical Models ◽  
Flood Control ◽  
Flood Management ◽  
Hydroelectric Power Station ◽  
Hydroelectric Power ◽  
Operating Characteristics ◽  
Hydro Power ◽  
Operation Modes ◽  
Wide Range ◽  
Environmental Requirements

The rapid spread of storm floods over large areas requires flood management throughout the river basin by the creation an innovative system of flood control facilities of various functional purposes distributed in the area. The central part of the system is the hydro system with hydro power plant. In addition, the flood control facilities on the side tributaries with self-regulating reservoir are included in the system. To assess the effect of controlling extreme water discharges by flood control facilities, it is necessary to develop special mathematical models reflecting the specifics of their operation. Unified mathematical models of the operation modes of a hydro complex with hydroelectric power station and flood control facility are created. They are implemented in a computer program that provides the ability to determine the main parameters and operating characteristics of hydro systems when performing multivariate calculations in a wide range of initial data. This makes possible specifying the parameters and operation modes of each hydro system with the current economic and environmental requirements, to assess the energy-economic and environmental consequences in the operation of the system of flood control facilities distributed in the area. The article analyses the results of the extreme water discharge’s regulation by the hydro system on the main river and flood control facilities on the side tributaries, considering environmental requirements.

scholarly journals Ring-Forming Polymerization toward Perfluorocyclobutyl and Ortho-Diynylarene-Derived Materials: From Synthesis to Practical Applications

Materials ◽  
2021 ◽  
Vol 14 (6) ◽  
pp. 1486
Author(s):  
Eugene B. Caldona ◽  
Ernesto I. Borrego ◽  
Ketki E. Shelar ◽  
Karl M. Mukeba ◽  
Dennis W. Smith
Keyword(s):  
Chemical Resistance ◽  
Structural Features ◽  
Review Article ◽  
Aryl Ether ◽  
Aromatic Rings ◽  
Practical Applications ◽  
Repeat Units ◽  
Wide Range ◽  
Synthetic Routes ◽  
The Cost

Many desirable characteristics of polymers arise from the method of polymerization and structural features of their repeat units, which typically are responsible for the polymer’s performance at the cost of processability. While linear alternatives are popular, polymers composed of cyclic repeat units across their backbones have generally been shown to exhibit higher optical transparency, lower water absorption, and higher glass transition temperatures. These specifically include polymers built with either substituted alicyclic structures or aromatic rings, or both. In this review article, we highlight two useful ring-forming polymer groups, perfluorocyclobutyl (PFCB) aryl ether polymers and ortho-diynylarene- (ODA) based thermosets, both demonstrating outstanding thermal stability, chemical resistance, mechanical integrity, and improved processability. Different synthetic routes (with emphasis on ring-forming polymerization) and properties for these polymers are discussed, followed by their relevant applications in a wide range of aspects.

scholarly journals Sensing of Nickel(II) Ions by Immobilizing Ligands and Using Different SPEs

2021 ◽  
Vol 6 (1) ◽  
pp. 2
Author(s):  
Liliana Anchidin-Norocel ◽  
Sonia Amariei ◽  
Gheorghe Gutt
Keyword(s):  
Bismuth Oxide ◽  
Human Population ◽  
Raw Materials ◽  
Sensor Technology ◽  
Cyclic Voltammogram ◽  
Accurate Analysis ◽  
Nickel Allergy ◽  
Nickel Ions ◽  
Practical Applications ◽  
Wide Range

The aim of this paper is the development of a sensor for the quantification of nickel ions in food raw materials and foods. It is believed that about 15% of the human population suffers from nickel allergy. In addition to digestive manifestations, food intolerance to nickel may also have systemic manifestations, such as diffuse dermatitis, diffuse itching, fever, rhinitis, headache, altered general condition. Therefore, it is necessary to control this content of nickel ions for the health of the human population by developing a new method that offers the advantages of a fast, not expensive, in situ, and accurate analysis. For this purpose, bismuth oxide-screen-printed electrodes (SPEs) and graphene-modified SPEs were used with a very small amount of dimethylglyoxime and amino acid L-histidine that were deposited. A potentiostat that displays the response in the form of a cyclic voltammogram was used to study the electrochemical properties of nickel standard solution with different concentrations. The results were compared and the most sensitive sensor proved to be bismuth oxide-SPEs with dimethylglyoxime (Bi2O3/C-dmgH2) with a linear response over a wide range (0.1–10 ppm) of nickel concentrations. Furthermore, the sensor shows excellent selectivity in the presence of common interfering species. The Bi2O3/C-dmgH2 sensor showed good viability for nickel analysis in food samples (cocoa, spinach, cabbage, and red wine) and demonstrated significant advancement in sensor technology for practical applications.

scholarly journals β-Lactoglobulin Adsorption Layers at the Water/Air Surface: 5. Adsorption Isotherm and Equation of State Revisited, Impact of pH

2021 ◽  
Vol 5 (1) ◽  
pp. 14
Author(s):  
Georgi G. Gochev ◽  
Volodymyr I. Kovalchuk ◽  
Eugene V. Aksenenko ◽  
Valentin B. Fainerman ◽  
Reinhard Miller
Keyword(s):  
Theoretical Description ◽  
Fluid Interfaces ◽  
Interfacial Behavior ◽  
Current State ◽  
Air Interface ◽  
Direct Measurements ◽  
Wide Range ◽  
Dilational Viscoelasticity ◽  
Parameter Values ◽  
Β Lactoglobulin

The theoretical description of the adsorption of proteins at liquid/fluid interfaces suffers from the inapplicability of classical formalisms, which soundly calls for the development of more complicated adsorption models. A Frumkin-type thermodynamic 2-d solution model that accounts for nonidealities of interface enthalpy and entropy was proposed about two decades ago and has been continuously developed in the course of comparisons with experimental data. In a previous paper we investigated the adsorption of the globular protein β-lactoglobulin at the water/air interface and used such a model to analyze the experimental isotherms of the surface pressure, Π(c), and the frequency-, f-, dependent surface dilational viscoelasticity modulus, E(c)f, in a wide range of protein concentrations, c, and at pH 7. However, the best fit between theory and experiment proposed in that paper appeared incompatible with new data on the surface excess, Γ, obtained from direct measurements with neutron reflectometry. Therefore, in this work, the same model is simultaneously applied to a larger set of experimental dependences, e.g., Π(c), Γ(c), E(Π)f, etc., with E-values measured strictly in the linear viscoelasticity regime. Despite this ambitious complication, a best global fit was elaborated using a single set of parameter values, which well describes all experimental dependencies, thus corroborating the validity of the chosen thermodynamic model. Furthermore, we applied the model in the same manner to experimental results obtained at pH 3 and pH 5 in order to explain the well-pronounced effect of pH on the interfacial behavior of β-lactoglobulin. The results revealed that the propensity of β-lactoglobulin globules to unfold upon adsorption and stretch at the interface decreases in the order pH 3 > pH 7 > pH 5, i.e., with decreasing protein net charge. Finally, we discuss advantages and limitations in the current state of the model.

scholarly journals A New Statistic for Detecting Genetic Differentiation

Genetics ◽  
2000 ◽  
Vol 155 (4) ◽  
pp. 2011-2014 ◽  
Author(s):  
Richard R Hudson
Keyword(s):  
Genetic Differentiation ◽  
Dna Sequences ◽  
Genetic Data ◽  
Island Model ◽  
Wide Range ◽  
Infinite Sites Model ◽  
Parameter Values

Abstract A new statistic for detecting genetic differentiation of subpopulations is described. The statistic can be calculated when genetic data are collected on individuals sampled from two or more localities. It is assumed that haplotypic data are obtained, either in the form of DNA sequences or data on many tightly linked markers. Using a symmetric island model, and assuming an infinite-sites model of mutation, it is found that the new statistic is as powerful or more powerful than previously proposed statistics for a wide range of parameter values.

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