scholarly journals An extension of the entropic chaos degree and its positive effect

2021 ◽  
Author(s):  
Kei Inoue ◽  
Tomoyuki Mao ◽  
Hidetoshi Okutomi ◽  
Ken Umeno
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponent ◽  
Initial Point ◽  
Estimation Methods ◽  
Dimensional Euclidean Space ◽  
Information Dynamics ◽  
Finite Space ◽  
Definition Of ◽  
Positive Effect ◽  
Chaos Degree

AbstractThe Lyapunov exponent is used to quantify the chaos of a dynamical system, by characterizing the exponential sensitivity of an initial point on the dynamical system. However, we cannot directly compute the Lyapunov exponent for a dynamical system without its dynamical equation, although some estimation methods do exist. Information dynamics introduces the entropic chaos degree to measure the strength of chaos of the dynamical system. The entropic chaos degree can be used to compute the strength of chaos with a practical time series. It may seem like a kind of finite space Kolmogorov-Sinai entropy, which then indicates the relation between the entropic chaos degree and the Lyapunov exponent. In this paper, we attempt to extend the definition of the entropic chaos degree on a d-dimensional Euclidean space to improve the ability to measure the stength of chaos of the dynamical system and show several relations between the extended entropic chaos degree and the Lyapunov exponent.

scholarly journals An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1511
Author(s):  
Kei Inoue
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Chaotic Maps ◽  
Chaotic Map ◽  
Calculation Formula ◽  
Two Dimensional ◽  
Information Dynamics ◽  
The Difference ◽  
Chaos Degree

The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps.

scholarly journals Geometric Algebra Framework Applied to Symmetrical Balanced Three-Phase Systems for Sinusoidal and Non-Sinusoidal Voltage Supply

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1259
Author(s):  
Francisco G. Montoya ◽  
Raúl Baños ◽  
Alfredo Alcayde ◽  
Francisco Manuel Arrabal-Campos ◽  
Javier Roldán Roldán Pérez
Keyword(s):  
Geometric Algebra ◽  
Dimensional Euclidean Space ◽  
Active Components ◽  
Electrical Circuits ◽  
Current Harmonics ◽  
Operation Conditions ◽  
Multiple Phase ◽  
Three Phase ◽  
Phase Systems ◽  
Definition Of

This paper presents a new framework based on geometric algebra (GA) to solve and analyse three-phase balanced electrical circuits under sinusoidal and non-sinusoidal conditions. The proposed approach is an exploratory application of the geometric algebra power theory (GAPoT) to multiple-phase systems. A definition of geometric apparent power for three-phase systems, that complies with the energy conservation principle, is also introduced. Power calculations are performed in a multi-dimensional Euclidean space where cross effects between voltage and current harmonics are taken into consideration. By using the proposed framework, the current can be easily geometrically decomposed into active- and non-active components for current compensation purposes. The paper includes detailed examples in which electrical circuits are solved and the results are analysed. This work is a first step towards a more advanced polyphase proposal that can be applied to systems under real operation conditions, where unbalance and asymmetry is considered.

scholarly journals Chaotic Dynamical Systems Associated with Tilings of RN

2011 ◽  
pp. 19-41
Author(s):  
Lionel Rosier
Keyword(s):  
Dynamical System ◽  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Homogeneous Space ◽  
Chaos Synchronization ◽  
Discrete Dynamical Systems ◽  
Dimensional Torus ◽  
Synchronization Mechanism ◽  
Chaotic Dynamical Systems ◽  
Regular Tiling

In this chapter, we consider a class of discrete dynamical systems defined on the homogeneous space associated with a regular tiling of RN, whose most familiar example is provided by the N-dimensional torus TN. It is proved that any dynamical system in this class is chaotic in the sense of Devaney, and that it admits at least one positive Lyapunov exponent. Next, a chaos-synchronization mechanism is introduced and used for masking information in a communication setup.

scholarly journals A VARIATIONAL FORMULATION OF SYMPLECTIC NONCOMMUTATIVE MECHANICS

2007 ◽  
Vol 04 (05) ◽  
pp. 789-805 ◽  
Author(s):  
IGNACIO CORTESE ◽  
J. ANTONIO GARCÍA
Keyword(s):  
Dynamical System ◽  
Phase Space ◽  
Variational Principle ◽  
Configuration Space ◽  
Variational Formulation ◽  
Noncommutative Space ◽  
First Order ◽  
Dynamical Properties ◽  
Definition Of ◽  
Space Noncommutativity

The standard lore in noncommutative physics is the use of first order variational description of a dynamical system to probe the space noncommutativity and its consequences in the dynamics in phase space. As the ultimate goal is to understand the inherent space noncommutativity, we propose a variational principle for noncommutative dynamical systems in configuration space, based on results of our previous work [18]. We hope that this variational formulation in configuration space can be of help to elucidate the definition of some global and dynamical properties of classical and quantum noncommutative space.

A Chaotification model based on sine and cosecant functions for enhancing chaos

2021 ◽  
Author(s):  
Yuqing Li ◽  
Xing He ◽  
Dawen Xia
Keyword(s):  
Fixed Point ◽  
Lyapunov Exponent ◽  
Chaotic Maps ◽  
Dynamic Properties ◽  
Chaotic Map ◽  
Sample Entropy ◽  
One Dimensional ◽  
Model Based ◽  
Chaotic Region ◽  
Definition Of

Chaotic maps with higher chaotic complexity are urgently needed in many application scenarios. This paper proposes a chaotification model based on sine and cosecant functions (CMSC) to improve the dynamic properties of existing chaotic maps. CMSC can generate a new map with higher chaotic complexity by using the existing one-dimensional (1D) chaotic map as a seed map. To discuss the performance of CMSC, the chaos properties of CMSC are analyzed based on the mathematical definition of the Lyapunov exponent (LE). Then, three new maps are generated by applying three classical 1D chaotic maps to CMSC respectively, and the dynamic behaviors of the new maps are analyzed in terms of fixed point, bifurcation diagram, sample entropy (SE), etc. The results of the analysis demonstrate that the new maps have a larger chaotic region and excellent chaotic characteristics.

scholarly journals Extracts from Artemisia vulgaris L. in Potato Cultivation—Preliminary Research on Biostimulating Effect

Agriculture ◽  
2020 ◽  
Vol 10 (8) ◽  
pp. 356 ◽  
Author(s):  
Pavol Findura ◽  
Sławomir Kocira ◽  
Patryk Hara ◽  
Anna Pawłowska ◽  
Agnieszka Szparaga ◽  
...  
Keyword(s):  
Metabolic Pathways ◽  
Total Concentration ◽  
Artemisia Vulgaris ◽  
Pilot Studies ◽  
Total Chlorophyll Content ◽  
Overall Evaluation ◽  
Potato Yields ◽  
Definition Of ◽  
Positive Effect

Nowadays the size and quality of potato yields is very important aspect in agriculture, due to the continuous climate change. Plants exposed to abiotic stress need new protection tools such as plant biostimulant. The new definition of this product include plant extracts as novel biostimulants. The aim of the study was to assess whether the extracts from Artemisia vulgaris L. would act as classic biostimulants, by affecting metabolic pathways. Since these are pilot studies, the content of chlorophyll, carotenoids, proline and polyphenols was chosen as indicators of changes in plants. The experiment was carried out under controlled environmental conditions on a very early cultivar Irys. The obtained results showed that foliar treatment of plants with extracts from Artemisia vulgaris L. had a positive effect on the increase of chlorophyll a and chlorophyll b content and its total concentration in potato leaves. The highest increase in the total chlorophyll content, amounting to 26.27% on average, was observed in plants sprayed with macerate at the dose of 0.6 mL·plant-1. Additionally, an increase in the carotenoids content was observed in plants sprayed with macerate. The study demonstrated that the polyphenols level was largely dependent on the method of extracts production and the dose of the tested extracts. Macerate and infusion applied in a higher dose induced in plants the changes in the concentration of polyphenols. The overall evaluation of the effectiveness of the tested preparations showed higher effectiveness of the macerate for all the analyzed traits.

scholarly journals A substrate-independent framework to characterize reservoir computers

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180723 ◽  
Author(s):  
Matthew Dale ◽  
Julian F. Miller ◽  
Susan Stepney ◽  
Martin A. Trefzer
Keyword(s):  
Dynamical System ◽  
Task Performance ◽  
Fading Memory ◽  
Reservoir Computing ◽  
Virtual Topology ◽  
Nonlinear Input ◽  
Definition Of ◽  
Substrate Independent ◽  
And Task

The reservoir computing (RC) framework states that any nonlinear, input-driven dynamical system (the reservoir ) exhibiting properties such as a fading memory and input separability can be trained to perform computational tasks. This broad inclusion of systems has led to many new physical substrates for RC. Properties essential for reservoirs to compute are tuned through reconfiguration of the substrate, such as change in virtual topology or physical morphology. As a result, each substrate possesses a unique ‘quality’—obtained through reconfiguration—to realize different reservoirs for different tasks. Here we describe an experimental framework to characterize the quality of potentially any substrate for RC. Our framework reveals that a definition of quality is not only useful to compare substrates, but can help map the non-trivial relationship between properties and task performance. In the wider context, the framework offers a greater understanding as to what makes a dynamical system compute, helping improve the design of future substrates for RC.

scholarly journals What is the dynamical hypothesis?

1998 ◽  
Vol 21 (5) ◽  
pp. 633-634 ◽  
Author(s):  
Nick Chater ◽  
Ulrike Hahn
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Turing Machines ◽  
Definition Of ◽  
Dynamical Hypothesis

Van Gelder's specification of the dynamical hypothesis does not improve on previous notions. All three key attributes of dynamical systems apply to Turing machines and are hence too general. However, when a more restricted definition of a dynamical system is adopted, it becomes clear that the dynamical hypothesis is too underspecified to constitute an interesting cognitive claim.

scholarly journals Shape Coherence and Finite-Time Curvature Evolution

2015 ◽  
Vol 25 (05) ◽  
pp. 1550076 ◽  
Author(s):  
Tian Ma ◽  
Erik M. Bollt
Keyword(s):  
Lyapunov Exponent ◽  
Dynamical Systems ◽  
Coherent Structures ◽  
Finite Time ◽  
Large Curvature ◽  
Nonautonomous Dynamical Systems ◽  
Finite Time Lyapunov Exponent ◽  
Close Proximity ◽  
Definition Of ◽  
Curvature Growth

We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal the dramatic change on shape such as the folding behaviors in a system. Closed trough curves of low finite-time curvature (FTC) evolution field indicate the existence of shape coherent sets, and troughs in the field indicate the most significant shape coherence. Here, we will demonstrate these properties of the FTC, as well as contrast to the popular Finite-Time Lyapunov Exponent (FTLE) computation, often used to indicate hyperbolic material curves as Lagrangian Coherent Structures (LCS). We show that often the FTC troughs are in close proximity to the FTLE ridges, but in other scenarios, the FTC indicates entirely different regions.

scholarly journals TAX STRUCTURE AND ECONOMIC GROWTH: DO DIFFERENCES IN INCOME LEVEL AND GOVERNMENT EFFECTIVENESS MATTER?

2018 ◽  
Vol 65 (01) ◽  
pp. 217-237 ◽  
Author(s):  
HALIT YANIKKAYA ◽  
TANER TURAN
Keyword(s):  
Low Income ◽  
Low Income Countries ◽  
Estimation Methods ◽  
Property Taxes ◽  
Tax Rates ◽  
Tax Structure ◽  
Tax Rate ◽  
Using Data ◽  
Positive Effect ◽  
Effect On Growth

We examine the effects of both overall tax rate and changes in tax structure on growth by using data for more than 100 high, middle, and low income countries by employing the GMM estimation methods. In general, our results do not support the argument that overall tax rates or changes in tax structure have a significant effect on growth. However, we find that a shift from income to consumption and property taxes leads to a positive and significant effect on growth rate while a shift from consumption and property taxes to income taxes has a positive effect for low-income countries.

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