scholarly journals Equilibria and Stability of One Class of Positive Dynamic Systems with Entropy Operator: Application to Investment Dynamics Modeling

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 859
Author(s):  
Yuri S. Popkov
Keyword(s):  
Dynamical Systems ◽  
Power Series ◽  
Dynamic Properties ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Stationary States ◽  
Existence Conditions ◽  
The Stability ◽  
Formal Power ◽  
Connectivity Parameter

Dynamical systems with entropy operator (DSEO) form a special class of dynamical systems whose nonlinear properties are described by the perturbed mathematical programming problem with entropy objective functions. A subclass of DSEO is the system with positive state coordinates (PDSEO), which are used as mathematical models of the spatiotemporal evolution of demographic and economic processes, dynamic image restoration procedures in computer tomography and machine learning. A mathematical model of the PDSEO with a connectivity parameter characterizing the influence of the entropy operator on the dynamic properties of the system is constructed. PDSEO can have positive stationary states of various classes depending on the number of positive components in the state vector. Classes with p positive components of the state vector ( p ≤ n , where n is the order of the system) are considered. The framework of formal power series and the method of successive approximations for the formation of existence conditions of stationary states are developed. The conditions of existence are obtained in the form of relations between the parameters of the system. We used the method of differential Bellman inequalities to study the stability of classes of stationary states in a limited region of phase space. The parametric conditions of instability of the zero stationary state and p positive stationary states depending on the connectivity parameter are obtained. The framework of formal power series and the method of successive approximations for the formation of existence conditions and classification of stationary states are developed. The stability conditions “in large” stationary states are obtained, based on the method of differential Bellman inequalities. The developed methods of existence, classification and stability are illustrated by the analysis of the dynamic properties of the economic model with stochastic investment exchange. Positive stationary states characterize the profitability of economic subsystems. The conditions of profitability and their stability for all subsystems in the system and their various groups are obtained.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

scholarly journals Global Stability and Dynamic Analysis for a Type of Macroeconomic Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Ya-Juan Yang ◽  
Ru-Fei Ma ◽  
Jing Zhang
Keyword(s):  
Dynamic Properties ◽  
Price System ◽  
Price Equation ◽  
Economic Systems ◽  
Dynamic Price ◽  
Existence Conditions ◽  
The Stability ◽  
Technical Operation ◽  
Special Case ◽  
Balanced Solution

This paper aims at the dynamic properties of the proposed globally planned economic systems named after CPE proposed by Loo-Keng Hua who is one of the worldwide famous Chinese mathematicians. First, we give new existence conditions of growth balanced solution to the model. Second, we lead into the concept of stability for balanced output and carry out a theorem that deals with some equivalent conditions for judging a solution of output starting from the fact that any initial input can whether approach the existing balanced solution or not. Third, a new dynamic price system related to interest factors is proposed here and it is demonstrated that the new price equation is a much generalized one in comparison with the original price one which is only a special case of this new price equation. Also, relationships of the balanced solutions between the price and the output equation are investigated and the stability analysis is studied as well for the new price system. Finally, two examples are employed to illustrate the technical operation of input-output method and some new contributions of this article.

scholarly journals Natural Frequencies of Axisymmetric Vibrations of Thin Hyperbolic Circular Plates with Clamped Edges

2017 ◽  
Vol 22 (2) ◽  
pp. 451-457
Author(s):  
J. Jaroszewicz
Keyword(s):  
Power Series ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Thickness Variation ◽  
Circular Plates ◽  
Clamped Edges ◽  
Analytical Frequency

Abstract A free vibration analysis of homogeneous and isotropic circular thin plates with nonlinear thickness variation and clamped edges is considered. The limited independent solutions of differential Euler equation were expanded in the power series based on the properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations.

A simulation apparatus for the experimental study of batch reactor control methods

1986 ◽  
Vol 51 (6) ◽  
pp. 1259-1267
Author(s):  
Josef Horák ◽  
Petr Beránek
Keyword(s):  
Experimental Study ◽  
Closed Loop ◽  
Dynamic Properties ◽  
Batch Reactor ◽  
Exothermic Reaction ◽  
Electric Heating ◽  
Batch Reactors ◽  
Exchange Area ◽  
The Stability ◽  
Methods Of Control

A simulation apparatus for the experimental study of the methods of control of batch reactors is devised. In this apparatus, the production of heat by an exothermic reaction is replaced by electric heating controlled by a computer in a closed loop; the reactor is cooled with an external cooler whose dynamic properties can be varied while keeping the heat exchange area constant. The effect of the cooler geometry on its dynamic properties is investigated and the effect of the cooler inertia on the stability and safety of the on-off temperature control in the unstable pseudostationary state is examined.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

Modal Analyses of Deployable Truss Structures Based on Shape Memory Polymer Composites

2016 ◽  
Vol 08 (07) ◽  
pp. 1640009 ◽  
Author(s):  
Fengfeng Li ◽  
Liwu Liu ◽  
Xin Lan ◽  
Tong Wang ◽  
Xiangyu Li ◽  
...  
Keyword(s):  
Finite Element ◽  
Shape Memory ◽  
Polymer Composites ◽  
Dynamic Properties ◽  
Low Cost ◽  
Shape Memory Polymer ◽  
Truss Structures ◽  
Modal Test ◽  
The Stability ◽  
Mechanical Devices

With large spatial deployable antennas used more widely, the stability of deployable antennas is attracting more attention. The form of the support structure is an important factor of the antenna’s natural frequency, which is essential to study to prevent the resonance. The deployable truss structures based on shape memory polymer composites (SMPCs) have made themselves feasible for their unique properties such as highly reliable, low-cost, light weight, and self-deployment without complex mechanical devices compared with conventional deployable masts. This study offers deliverables as follows: an establishment of three-longeron beam and three-longeron truss finite element models by using ABAQUS; calculation of natural frequencies and vibration modes; parameter studies for influence on their dynamic properties; manufacture of a three-longeron truss based on SMPC, and modal test of the three-longeron truss. The results show that modal test and finite element simulation fit well.

scholarly journals On transformations of formal power series

2003 ◽  
Vol 184 (2) ◽  
pp. 369-383 ◽  
Author(s):  
Manfred Droste ◽  
Guo-Qiang Zhang
Keyword(s):  
Power Series ◽  
Formal Power Series ◽  
Formal Power
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