nonlinear difference equations of higher order are important in applications; such equations appear naturally as discrete analogues of differential and delay differential equations which model various diverse phenomena in biology, ecology, economics, physics and engineering. the study of dynamical properties of such equations is of great importance in many areas. the autonomous difference equat...

In this paper, a neural network model reference adaptive system speed observer is designed, which can be used in speed control of linear induction motors (LIMs). Dynamical equations of LIM have been considered accurate. In other words, the end effect and the electrical losses of the motor have been included in the motor equivalent circuit. Then equations of the reference model and adaptive mode...

The trigonometric KZ equations associated with a Lie algebra g depend on a parameter λ ∈ h where h ⊂ g is the Cartan subalgebra. We suggest a system of dynamical difference equations with respect to λ compatible with the KZ equations. The dynamical equations are constructed in terms of intertwining operators of g -modules.

This paper demonstrates the feasibility of modeling any dynamical system using a set of fractional order differential equations, including distributed and lumped systems. Fractional order differentiators and integrators are the basic elements of these equations representing the real model of the dynamical system, which in turn implies the necessity of using fractional order controllers instead ...

In this research, dynamic analysis of the rotational slender axially moving string is investigated. String assumed as Euler Bernoulli beam. The axial motion of the string, gyroscopic force and mass eccentricity were considered in the study. Equations of motion are derived using Hamilton’s principle, resulting in two partial differential equations for the transverse motions. The equations are ch...

In this paper we introduce some stability criteria for impulsive fuzzy system of differential equations with finite delay in states. Firstly, a new comparison principle for fuzzy differential system compared to crisp ordinary differential equation, based on a notion of upper quasi-monotone nondecreasing, in N dimentional state space is presented. Furthermore, in order to analyze the stability o...

Weak interactions of solitary waves in the generalized nonlinear Schrödinger equations are studied. It is first shown that these interactions exhibit similar fractal dependence on initial conditions for different nonlinearities. Then by using the Karpman-Solov'ev method, a universal system of dynamical equations is derived for the velocities, amplitudes, positions, and phases of interacting sol...

In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier–Stokes equations on the rotating 2-dimensional sphere. Then we show the existence of an asymptotically compact random dynamical system associated with the equations.

The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system.

Abstract. It is known that some equations of differential geometry are derived from variational principle in form of Euler-Lagrange equations. The equations of geodesic flow in Riemannian geometry is an example. Conversely, having Lagrangian dynamical system in a manifold, one can consider it as geometric equipment of this manifold. Then properties of other dynamical systems can be studied rela...