Multiple–scale Analysis of Dynamical Systems on the Lattice
نویسنده
چکیده
We propose a new approach to the multiple–scale analysis of difference equations, in the context of the finite operator calculus. We derive the transformation formulae that map any given dynamical system, continuous or discrete, into a rescaled discrete system, by generalizing a classical result due to Jordan. Under suitable analytical hypotheses on the function space we consider, the rescaled equations are of finite order. Our results are applied to the study of multiple–scale reductions of dynamical systems, and in particular to the case of the Duffing equation.
منابع مشابه
Dynamical Behavior of a Rigid Body with One Fixed Point (Gyroscope). Basic Concepts and Results. Open Problems: a Review
The study of the dynamic behavior of a rigid body with one fixed point (gyroscope) has a long history. A number of famous mathematicians and mechanical engineers have devoted enormous time and effort to clarify the role of dynamic effects on its movement (behavior) – stable, periodic, quasi-periodic or chaotic. The main objectives of this review are: 1) to outline the characteristic features of...
متن کاملInvestigation of Dynamical Behavior (Transverse Vibration) and Instability Analysis of Carbon Nanotubes Conveying Nanofluid
This work focuses on the dynamical behavior of carbon nanotubes, including vibration, wave propagation and fluid-structure interaction. In the present research, transverse vibration of nano fluid conveying carbon nanotubes is investigated. To this end, based on the nonlocal and strain-inertia gradient continuum elasticity theories and by using rod and Euler-Bernoulli beam models, the system’s d...
متن کاملThe Study of Nonlinear Dynamical Systems Nuclear Fission Using Hurwitz Criterion
In this paper, the nonlinear dynamic system of equations, a type of nuclear ssion reactor is solved analytically and numerically. Considering that the direct solution of three-dimensional dynamical systems analysis and more in order to determine the stability and instability, in terms of algebraicsystems is dicult. Using certain situations in mathematics called Hurwitz criterion, Necessary and ...
متن کاملFractional dynamical systems: A fresh view on the local qualitative theorems
The aim of this work is to describe the qualitative behavior of the solution set of a given system of fractional differential equations and limiting behavior of the dynamical system or flow defined by the system of fractional differential equations. In order to achieve this goal, it is first necessary to develop the local theory for fractional nonlinear systems. This is done by the extension of...
متن کاملData Envelopment Analysis from simulation on the Lattice QCD using CCR model
One of the most serious principles in production theory in economic is the principle of "efficiency". Simply put, efficiency can be defined as the demand that the desired goals (outputs) are achieved with the minimum use of the available resources (inputs). In order to, distinguish the relative efficiency of organizational units with multiple inputs to produce multiple outputs, "Data Envelopmen...
متن کامل