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Parallelisms between differential and difference equations

Veronika Chrastinová, Václav Tryhuk (2012)

Mathematica Bohemica

The paper deals with the higher-order ordinary differential equations and the analogous higher-order difference equations and compares the corresponding fundamental concepts. Important dissimilarities appear for the moving frame method.

Partial generalized synchronization theorems of differential and discrete systems

Jianyi Jing, Lequan Min, Geng Zhao (2008)

Kybernetika

This paper presents two theorems for designing controllers to achieve directional partial generalized synchronization (PGS) of two independent (chaotic) differential equation systems or two independent (chaotic) discrete systems. Two numerical simulation examples are given to illustrate the effectiveness of the proposed theorems. It can be expected that these theorems provide new tools for understanding and studying PGS phenomena and information encryption.

Perfect observers for fractional discrete-time linear systems

Ewa Pawluszewicz (2016)

Kybernetika

A perfect (exact) fractional observer of discrete-time singular linear control system of fractional order is studied. Conditions for its existence are given. The obtained results are applied to the detectability problem of the class of systems under consideration.

Periodic solutions of a class of third-order differential equations with two delays depending on time and state

Rabah Khemis, Abdelouaheb Ardjouni, Ahlème Bouakkaz, Ahcene Djoudi (2019)

Commentationes Mathematicae Universitatis Carolinae

The goal of the present paper is to establish some new results on the existence, uniqueness and stability of periodic solutions for a class of third order functional differential equations with state and time-varying delays. By Krasnoselskii's fixed point theorem, we prove the existence of periodic solutions and under certain sufficient conditions, the Banach contraction principle ensures the uniqueness of this solution. The results obtained in this paper are illustrated by an example.

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