A Class of Hyperspace Systems and Distributional Chaos

2014 ◽  
Vol 670-671 ◽  
pp. 1570-1572
Author(s):  
Wei Wang ◽  
Xiao Gang Zhu
Keyword(s):  
Dynamical System ◽  
Difference Equation ◽  
Agricultural Production ◽  
Irrigation District ◽  
Corn Yield ◽  
Primitive Substitution ◽  
Yield Analysis ◽  
Distributional Chaos ◽  
Dynamical Properties ◽  
Ecological Difference

Research on dynamical system has penetrated into many problems of agricultural production, such as prediction of corn yield, analysis on operational situation of irrigation district and research on ecological difference equation. In this paper, we investigated dynamical properties for non-primitive substitution and the set-valued maps induced by the substitution. We proved In two cases that the hyperspace systems induced by non-primitive substitution are not distributional chaotic.

Two Simplest Quadratic Chaotic Maps Without Equilibrium

2018 ◽  
Vol 28 (12) ◽  
pp. 1850144 ◽  
Author(s):  
Shirin Panahi ◽  
Julien C. Sprott ◽  
Sajad Jafari
Keyword(s):  
Dynamical System ◽  
Bifurcation Diagram ◽  
Lyapunov Exponents ◽  
Chaotic Maps ◽  
Basin Of Attraction ◽  
Hidden Attractor ◽  
Return Map ◽  
Right Hand ◽  
Dynamical Properties ◽  
The Right

Two simple chaotic maps without equilibria are proposed in this paper. All nonlinearities are quadratic and the functions of the right-hand side of the equations are continuous. The procedure of their design is explained and their dynamical properties such as return map, bifurcation diagram, Lyapunov exponents, and basin of attraction are investigated. These maps belong to the hidden attractor category which is a newly introduced category of dynamical system.

scholarly journals Communicating vessels: a non-linear dynamical system

2017 ◽  
Vol 39 (3) ◽  
Author(s):  
Roberto De Luca ◽  
Orazio Faella
Keyword(s):  
Dynamical System ◽  
Fluid Flow ◽  
Ideal Fluid ◽  
Oscillatory Motion ◽  
Linear Dynamical System ◽  
Static Properties ◽  
Bernoulli’S Equation ◽  
Non Linear ◽  
Dynamical Properties

The dynamics of an ideal fluid contained in two communicating vessels is studied. Despite the fact that the static properties of this system have been known since antiquity, the knowledge of the dynamical properties of an ideal fluid flowing in two communicating vessels is not similarly widespread. By means of Bernoulli's equation for non-stationary fluid flow, we study the oscillatory motion of the fluid when dissipation can be neglected.

scholarly journals Spatial distribution of the exchangeable base ratios in the soils of the R.U.T. irrigation district

2017 ◽  
Vol 70 (1) ◽  
pp. 8077-8084
Author(s):  
Carlos José López Martínez ◽  
Andrés Echeverri Sanchez ◽  
Juan Carlos Menjivar Flores
Keyword(s):  
Spatial Distribution ◽  
Agricultural Production ◽  
Central Area ◽  
Exchange Capacity ◽  
Potassium Deficiency ◽  
Irrigation District ◽  
Semivariogram Model ◽  
Exchangeable Magnesium ◽  
Ionic Imbalance ◽  
Best Fit

One of the more important agricultural production centers in Colombia is the R.U.T. Irrigation District, located in the Valle de Cauca. This study evaluated the spatial distribution of ratios of Ca2+, Mg2+, Na+ and K+, along with the percentage of saturation of these bases in the cation exchange capacity. 100 samples were taken at two depths to determine the EC, pH, Ca2+, Mg2+, Na+ and K+. The interpolations were made using the Geostatistical Analyst extension of ArcGis 10.3.1. The best fit semivariogram model was used, obtaining a raster surface with values of each chemical property, with which the plans were generated. The central area of the (La Union) irrigation district was more affected, with percentages of exchangeable magnesium between 40% and 75%, an inverted Ca2+/Mg2+ ratio, and a low calcium saturation percentage. The ratios were high for Mg2+/K+, normal for K+/Mg2+, high for Ca2+/K+, and broad for (Ca2+ + Mg2+)/K+, indicating a probable potassium deficiency that affected fertility. An ionic imbalance in the exchange complex was evident in the main bases of change, which may indicate degradation processes for fertility.

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.

Dynamics of Neural Networks as Nonlinear Systems with Several Equilibria

2011 ◽  
pp. 331-357 ◽  
Author(s):  
Daniela Danciu
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Neural Networks ◽  
Time Delay ◽  
Dynamical Systems ◽  
Qualitative Properties ◽  
The Neural Network ◽  
The Neural Networks ◽  
Global Asymptotics ◽  
Dynamical Properties

Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. The chapter deals with the second kind of dynamics. More precisely, since the emergent computational capabilities of a recurrent neural network can be achieved provided it has suitable dynamical properties when viewed as a system with several equilibria, the chapter deals with those qualitative properties connected to the achievement of such dynamical properties as global asymptotics and gradient-like behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance with the state of the art of the theory of time delay dynamical systems.

Study on the Relationship between Soil Nutrient and Yield Analysis Based on Bivariate Correlation between

2014 ◽  
Vol 998-999 ◽  
pp. 1466-1469
Author(s):  
Li Ying Cao ◽  
Xiao Xian Zhang ◽  
Yue Ling Zhao ◽  
Gui Fen Chen
Keyword(s):  
Soil Nutrient ◽  
Nutrient Content ◽  
Maize Yield ◽  
Nutrient Level ◽  
Corn Yield ◽  
Yield Analysis ◽  
Bivariate Correlation ◽  
Plot Yield ◽  
The Relationship ◽  
Nitrogen Phosphorus

Soil nutrient level is an important factor affecting the yield of corn, to find out the effect of nitrogen, phosphorus, potassium on maize yield, analysis of bivariate correlation in SPSS based on the relationship between nutrient content, nitrogen, phosphorus, potassium in the plot and each plot yield directly was analyzed, the experimental results show that it doesn't matter: P, K and the yield of corn, corn yield and nitrogen related.

On an extension of Mycielski’s theorem and invariant scrambled sets

2014 ◽  
Vol 36 (2) ◽  
pp. 632-648 ◽  
Author(s):  
FENG TAN
Keyword(s):  
Dynamical System ◽  
Polish Space ◽  
Invariant Relation ◽  
Invariant Subset ◽  
Residual Subset ◽  
Continuous Map ◽  
Dynamical Properties ◽  
Do So

Let $(X,f)$ be a dynamical system, where $X$ is a perfect Polish space and $f:X\rightarrow X$ is a continuous map. In this paper we study the invariant dependent sets of a given relation string ${\it\alpha}=\{R_{1},R_{2},\ldots \}$ on $X$. To do so, we need the relation string ${\it\alpha}$ to satisfy some dynamical properties, and we say that ${\it\alpha}$ is $f$-invariant (see Definition 3.1). We show that if ${\it\alpha}=\{R_{1},R_{2},\ldots \}$ is an $f$-invariant relation string and $R_{n}\subset X^{n}$ is a residual subset for each $n\geq 1$, then there exists a dense Mycielski subset $B\subset X$ such that the invariant subset $\bigcup _{i=0}^{\infty }f^{i}B$ is a dependent set of $R_{n}$ for each $n\geq 1$ (see Theorems 5.4 and 5.5). This result extends Mycielski’s theorem (see Theorem A) when $X$ is a perfect Polish space (see Corollary 5.6). Furthermore, in two applications of the main results, we simplify the proofs of known results on chaotic sets in an elegant way.

scholarly journals Stability of a time discrete perturbed dynamical system with delay

1999 ◽  
Vol 3 (1) ◽  
pp. 57-63 ◽  
Author(s):  
Michael I. Gil' ◽  
Sui Sun Cheng
Keyword(s):  
Dynamical System ◽  
Positive Integer ◽  
Difference Equation ◽  
Absolute Stability ◽  
Nonlinear Difference Equation ◽  
Stability Conditions ◽  
System With Delay ◽  
Equation With Delay

LetCnbe the set ofncomplex vectors endowed with a norm‖⋅‖Cn. LetA,Bbe two complexn×nmatrices andτa positive integer. In the present paper we consider the nonlinear difference equation with delay of the typeuk+1=Auk+Buk−τ+Fk(uk,uk−τ),      k=0,1,2,…, whereFk:Cn×Cn→Cnsatisfies the condition‖Fk(x,y)‖Cn≤p‖x‖Cn+q‖y‖Cn,       k=0,1,2,…, wherepandqare positive constants. In this paper, absolute stability conditions for this equation are established.

scholarly journals Quantifying the impacts of compound extremes on agriculture

2021 ◽  
Vol 25 (2) ◽  
pp. 551-564
Author(s):  
Iman Haqiqi ◽  
Danielle S. Grogan ◽  
Thomas W. Hertel ◽  
Wolfram Schlenker
Keyword(s):  
Heat Stress ◽  
Water Stress ◽  
Agricultural Production ◽  
Hydrological Model ◽  
The United States ◽  
Food Prices ◽  
Yield Response ◽  
Corn Yield ◽  
Comprehensive Understanding ◽  
Wet Heat

Abstract. Agricultural production and food prices are affected by hydroclimatic extremes. There has been a growing amount of literature measuring the impacts of individual extreme events (heat stress or water stress) on agricultural and human systems. Yet, we lack a comprehensive understanding of the significance and the magnitude of the impacts of compound extremes. This study combines a fine-scale weather product with outputs of a hydrological model to construct functional metrics of individual and compound hydroclimatic extremes for agriculture. Then, a yield response function is estimated with individual and compound metrics, focusing on corn in the United States during the 1981–2015 period. Supported by statistical evidence, the findings suggest that metrics of compound hydroclimatic extremes are better predictors of corn yield variations than metrics of individual extremes. The results also confirm that wet heat is more damaging than dry heat for corn. This study shows the average yield damage from heat stress has been up to four times more severe when combined with water stress.

scholarly journals Reiterative Distributional Chaos on Banach Spaces

2019 ◽  
Vol 29 (14) ◽  
pp. 1950201 ◽  
Author(s):  
Antonio Bonilla ◽  
Marko Kostić
Keyword(s):  
Banach Spaces ◽  
Continuous Linear Operator ◽  
Linear Operators ◽  
Nonzero Vector ◽  
Vector Subspace ◽  
Continuous Linear ◽  
Distributional Chaos ◽  
Dynamical Properties ◽  
Definition Of ◽  
Continuous Linear Operators

If we change the upper and lower densities in the definition of distributional chaos of a continuous linear operator on a Banach space [Formula: see text] by the Banach upper and Banach lower densities, respectively, we obtain Li–Yorke chaos. Motivated by this, we introduce the notions of reiterative distributional chaos of types [Formula: see text], [Formula: see text] and [Formula: see text] for continuous linear operators on Banach spaces, which are characterized in terms of the existence of an irregular vector with additional properties. Moreover, we study its relations with other dynamical properties and present the conditions for the existence of a vector subspace [Formula: see text] of [Formula: see text], such that every nonzero vector in [Formula: see text] is both irregular for [Formula: see text] and distributionally near zero for [Formula: see text].

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