相关论文: Folding, Cycles and Chaos in Discrete Planar Syste…

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…

In the paper below we consider a problem of stabilization of a priori unknown unstable periodic orbits in non-linear autonomous discrete dynamical systems. We suggest a generalization of a non-linear DFC scheme to improve the rate of…

In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…

It is known that discrete scale invariance leads to log-periodic corrections to scaling. We investigate the correlations of a system with discrete scale symmetry, discuss in detail possible extension of this symmetry such as translation and…

We consider the dynamics of systems of self propelling particles with nonholonomic constraints. A continuum model for a discrete algorithm used in works by T. Vicsek et al. is proposed. For a case of planar geometry the finite flocking…

This work deals with planar dynamical systems with and without noise. In the first part, we seek to gain a refined understanding of such systems by studying their differential-geometric transformation properties under an arbitrary smooth…

An exact discretization method is being developed for solving linear systems of ordinary fractional-derivative differential equations with constant matrix coefficients (LSOFDDECMC). It is shown that the obtained linear discrete system in…

We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of…

We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, focussing in particular on reachability, model-checking, and invariant-generation questions, both unconditionally as well as relative to…

The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…

Nearly all nontrivial real-world systems are nonlinear dynamical systems. Chaos describes certain nonlinear dynamical systems that have a very sensitive dependence on initial conditions. Chaotic systems are always deterministic and may be…

In this paper we study the family of planar hybrid differential systems formed by two linear centers and a polynomial reset map of any degree. We study their limit cycles and also provide examples of these hybrid systems exhibiting chaotic…

Polynomial chaos is a powerful technique for propagating uncertainty through ordinary and partial differential equations. Random variables are expanded in terms of orthogonal polynomials and differential equations are derived for the…

We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…

We consider two stable heteroclinic cycles rotating in opposite directions, coupled via diffusive terms. A complete synchronization in this system is impossible, and numerical exploration shows that chaos is abundant at low levels of…

This paper deals with fractional-order controlled systems and fractional-order controllers in the discrete domain. The mathematical description by the fractional difference equations and properties of these systems are presented. A…

Using the predictor-corrector scheme, the fractional order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional order diffusionless system for variation of the single control parameter is…

Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…

We present a method of discrete modeling and analysis of multilevel dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. Architectural model of information system supporting simulation…

The dynamics of a linear dynamical system over a finite field can be described by using the elementary divisors of the corresponding matrix. It is natural to extend the investigation to a general finite commutative ring. In a previous…