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 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.

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.

Unbounded Linear Operators

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Hilbert Spaces ◽  
Linear Operators ◽  
Von Neumann ◽  
Limit Circle ◽  
Sectorial Operators ◽  
Closed Operators ◽  
The Stability ◽  
Symmetric Operators ◽  
Unbounded Linear Operators ◽  
Special Case

This chapter is concerned with closable and closed operators in Hilbert spaces, especially with the special classes of symmetric, J-symmetric, accretive and sectorial operators. The Stone–von Neumann theory of extensions of symmetric operators is treated as a special case of results for compatible adjoint pairs of closed operators. Also discussed in detail is the stability of closedness and self-adjointness under perturbations. The abstract results are applied to operators defined by second-order differential expressions, and Sims’ generalization of the Weyl limit-point, limit-circle characterization for symmetric expressions to J-symmetric expressions is proved.

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.

Existence of Periodic Solution for Equation of Motion of Simple Beams With Harmonically Variable Length

1995 ◽  
Author(s):  
Ebrahim Esmailzadeh ◽  
Gholamreza Nakhaie-Jazar ◽  
Bahman Mehri
Keyword(s):  
Periodic Solution ◽  
Fixed Point ◽  
Nonlinear Function ◽  
Axial Direction ◽  
Equation Of Motion ◽  
The Other ◽  
Sufficient Condition ◽  
Vibrating String ◽  
The Stability ◽  
Special Case

Abstract The transverse vibrating motion of a simple beam with one end fixed while driven harmonically along its axial direction from the other end is investigated. For a special case of zero value for the rigidity of the beam, the system reduces to that of a vibrating string with the corresponding equation of its motion. The sufficient condition for the periodic solution of the beam is then derived by means of the Green’s function and Schauder’s fixed point theorem. The criteria for the stability of the system is well defined and the condition for which the performance of the beam behaves as a nonlinear function is stated.

1. On Cases of Instability in Open Structures

1888 ◽  
Vol 14 ◽  
pp. 106-106
Author(s):  
E. Sang
Keyword(s):  
Linear Structures ◽  
Symmetric Structure ◽  
Linear Resistance ◽  
Open Structures ◽  
Extensive Class ◽  
The Subject ◽  
The Stability ◽  
Special Case

AbstractIn the course of some remarks on the design proposed for the Forth Bridge, the author of this paper had enunciated the remarkable theorem, that any symmetric structure built on a rectangular base, and depending on linear resistance alone, is necessarily unstable. The proof of it, given in the eleventh volume of the Transactions of the Royal Scottish Society of Arts, is derived from considerations affecting the special case; but this theorem is only one of an extensive class, and therefore the subject of instability among linear structures in general is here taken up.In the case of regular or semi-regular arrangements, having the corners of an upper supported from the corners of an under polygon, it is shown that when the figures are of odd numbers the structures are stable, while those with even numbers are unstable ; unless indeed the polygons be placed conformably, in which case the stability extends to both classes.

scholarly journals MONETARY POLICY IN AN ISLAMIC ECONOMICS

2021 ◽  
Vol 9 (5) ◽  
pp. 315-326
Author(s):  
Bismi Khalidin
Keyword(s):  
Monetary Policy ◽  
Discount Rate ◽  
General Concept ◽  
Economic Systems ◽  
Open Market ◽  
Holy Quran ◽  
Market Operation ◽  
The Holy Quran ◽  
Open Market Operation ◽  
The Stability

The primary aim of this paper is to elucidate the general concept of monetary policy under Islamic Economics. Not only does the stability of but also the growth of the economy in a country strongly depends upon monetary policy implemented. Such the phenomenon also prevails in Islamic Economics in which the term is also ruled by the Holy Quran and the Hadith of the Prophet. Moreover, the Prophet issued some regulations regarding monetary, such as to adopt Dinars and as the Islamic currencies. It is noted that, however, the thing distinguishing between Islamic Economics and other economic systems the variable of interest or usury, where either the Holy Quran or the Hadith clearly states that it is banned. Due to using interest as the yardstick, the conventional monetary instruments such as Open Market Operation, Discount Rate and the likes are not considered as the monetary instruments under Islamic Economics. Therefore, Instead of interest, Islamic Economics adopts Profit Loss Sharing (PLS) system, regarded as the important part of monetary policy. Moreover, Islamic Economics has also its specific monetary standard and instruments, which are far from interest or variables, such as certificates and others.

scholarly journals Controlled Positive Dynamic Systems with an Entropy Operator: Fundamentals of the Theory and Applications

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2585
Author(s):  
Yuri S. Popkov
Keyword(s):  
Feedback Control ◽  
Dynamic Systems ◽  
Dynamic Properties ◽  
Monotone Operators ◽  
Singular Points ◽  
Program Control ◽  
Linear Feedback ◽  
Economic Systems ◽  
Linear Feedback Control ◽  
Nonzero Equilibrium

Controlled dynamic systems with an entropy operator (DSEO) are considered. Mathematical models of such systems were used to study the dynamic properties in demo-economic systems, the spatiotemporal evolution of traffic flows, recurrent procedures for restoring images from projections, etc. Three problems of the study of DSEO are considered: the existence and uniqueness of singular points and the influence of control on them; stability in “large” of the singular points; and optimization of program control with linear feedback. The theorems of existence, uniqueness, and localization of singular points are proved using the properties of equations with monotone operators and the method of linear majorants of the entropy operator. The theorem on asymptotic stability of the DSEO in “large” is proven using differential inequalities. Methods for the synthesis of quasi-optimal program control and linear feedback control with integral quadratic quality functional, and ensuring the existence of a nonzero equilibrium, were developed. A recursive method for solving the integral equations of the DSEO using the multidimensional functional power series and the multidimensional Laplace transform was developed. The problem of managing regional foreign direct investment is considered, the distribution of flows is modeled by the corresponding DSEO. It is shown that linear feedback control is a more effective tool than program control.

Asymptotic Behavior of Periodic Cohen-Grossberg Neural Networks with Delays

2009 ◽  
Vol 21 (12) ◽  
pp. 3444-3459 ◽  
Author(s):  
Wei Lin
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Lyapunov Method ◽  
Autonomous Systems ◽  
Neural Systems ◽  
Stability Criteria ◽  
Volterra System ◽  
Numerical Examples ◽  
The Stability ◽  
Special Case

Without assuming the positivity of the amplification functions, we prove some M-matrix criteria for the [Formula: see text]-global asymptotic stability of periodic Cohen-Grossberg neural networks with delays. By an extension of the Lyapunov method, we are able to include neural systems with multiple nonnegative periodic solutions and nonexponential convergence rate in our model and also include the Lotka-Volterra system, an important prototype of competitive neural networks, as a special case. The stability criteria for autonomous systems then follow as a corollary. Two numerical examples are provided to show that the limiting equilibrium or periodic solution need not be positive.

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