Distribution of values of linear functions and asymptotic behavior of trajectories of some dynamical systems

1995 ◽  
Vol 58 (3) ◽  
pp. 948-959 ◽  
Author(s):  
N. G. Moshchevitin
Keyword(s):  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Linear Functions ◽  
Distribution Of Values

scholarly journals Family of controllers based on sector non-linear functions: an application for first-order dynamical systems

2020 ◽  
Vol 14 (10) ◽  
pp. 1387-1392
Author(s):  
Marlen Meza-Sánchez ◽  
Maria del Carmen Rodríguez-Liñán ◽  
Eddie Clemente
Keyword(s):  
Dynamical Systems ◽  
Linear Functions ◽  
First Order ◽  
Non Linear

Activities: Iterating Linear Functions—An Introduction to Dynamical Systems

1997 ◽  
Vol 90 (2) ◽  
pp. 122-136
Author(s):  
Jonathan Choate
Keyword(s):  
Mathematics Education ◽  
Dynamical Systems ◽  
Numerical Methods ◽  
Mathematics Curriculum ◽  
Secondary Mathematics ◽  
Linear Functions ◽  
Exponential Functions ◽  
Numerical Iteration ◽  
Symbolic Methods ◽  
And Mathematics

The arrival of computers has caused some major changes in both mathematics and mathematics education. One of the biggest shifts has been from an emphasis on symbolic methods to one on numerical methods. One field of mathematics, dynamical systems, requires considerable number crunching and is just coming into its own because we currently have the ability to perform extensive calculations easily. This article introduces students to this new field. The study of sequences created by using numerical iteration provides interesting new ways to approach many of the concepts central to the secondary mathematics curriculum, such as functions in general and linear and exponential functions in particular.

scholarly journals Asymptotics for some discretizations of dynamical systems, application to second order systems with non-local nonlinearities

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Thierry Horsin ◽  
Mohamed Ali Jendoubi
Keyword(s):  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Equilibrium Points ◽  
Infinite Dimensional ◽  
Infinite Dimensional Dynamical Systems ◽  
Finite Dimensional ◽  
Angle Condition ◽  
Non Local ◽  
Second Order Systems

<p style='text-indent:20px;'>In the present paper we study the asymptotic behavior of discretized finite dimensional dynamical systems. We prove that under some discrete angle condition and under a Lojasiewicz's inequality condition, the solutions to an implicit scheme converge to equilibrium points. We also present some numerical simulations suggesting that our results may be extended under weaker assumptions or to infinite dimensional dynamical systems.</p>

RAPID GROWTH PATHS IN CONVEX-VALUED RANDOM DYNAMICAL SYSTEMS

2001 ◽  
Vol 01 (04) ◽  
pp. 493-509 ◽  
Author(s):  
IGOR V. EVSTIGNEEV ◽  
MICHAEL I. TAKSAR
Keyword(s):  
Economic Growth ◽  
Asymptotic Behavior ◽  
Dynamical Systems ◽  
Growth Rates ◽  
Stochastic Models ◽  
Rapid Growth ◽  
Random Dynamical Systems ◽  
Random Vectors ◽  
Time Period

This paper examines set-valued random dynamical systems defined by convex homogeneous stochastic operators. The operators under consideration transform elements of a cone contained in a space of random vectors into subsets of the cone. We study rapid paths of such dynamical systems, i.e. those paths which maximize (appropriately defined) growth rates at every time period. Questions of existence, uniqueness and asymptotic behavior of infinite rapid trajectories are considered. The study is motivated by problems related to stochastic models of economic growth.

Sign in / Sign up

Export Citation Format

Share Document