scholarly journals Periodic solutions of a discrete-time diffusive system governed by backward difference equations

2005 ◽  
Vol 2005 (3) ◽  
pp. 586218 ◽  
Author(s):  
Binxiang Dai ◽  
Jiezhong Zou
Keyword(s):  
Periodic Solutions ◽  
Discrete Time ◽  
Difference Equations ◽  
Diffusive System

A Theory of Index for Point Mapping Dynamical Systems

1980 ◽  
Vol 47 (1) ◽  
pp. 185-190 ◽  
Author(s):  
C. S. Hsu
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Systems ◽  
Periodic Solutions ◽  
Discrete Time ◽  
Difference Equations ◽  
Vector Fields ◽  
Time Difference ◽  
Point Mapping ◽  
Strongly Nonlinear

Dynamical systems governed by discrete time-difference equations are referred to as point mapping dynamical systems in this paper. Based upon the Poincare´ theory of index for vector fields, a theory of index is established for point mapping dynamical systems. Besides its intrinsic theoretic value, the theory can be used to help search and locate periodic solutions of strongly nonlinear systems.

scholarly journals On strongly irregular periodic solutions of the linear nonhomogeneous discrete equation of the first order

2020 ◽  
Vol 56 (1) ◽  
pp. 30-35
Author(s):  
A. K. Demenchuk
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Periodic Solutions ◽  
Discrete Time ◽  
Difference Equations ◽  
Prime Numbers ◽  
Discrete Equation ◽  
Linear Difference Equations ◽  
First Order ◽  
Discrete Equations

As is proved earlier (the Massera theorem), the first-order scalar periodic ordinary differential equation does not have strongly irregular periodic solutions (solutions with a period incommensurable with the period of the equation). For difference equations with discrete time, strong irregularity means that the equation period and the period of its solution are relatively prime numbers. It is known that in the case of discrete equations, the mentioned result has no complete analog.The purpose of this paper is to investigate the possibility of realizing an analog of the Massera theorem for certain classes of difference equations. To do this, we consider the class of linear difference equations. It is proved that a linear nonhomogeneous non-stationary periodic discrete equation of the first order does not have strongly irregular non-stationary periodic solutions.

scholarly journals Two periodic solutions of neutral difference equations modelling physiological processes

2006 ◽  
Vol 2006 ◽  
pp. 1-12 ◽  
Author(s):  
Jun Wu ◽  
Yicheng Liu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Periodic Solutions ◽  
Point Theorem ◽  
Difference Equations ◽  
Neutral Difference Equations ◽  
First Order ◽  
Analysis Techniques ◽  
Physiological Processes

We establish existence, multiplicity, and nonexistence of periodic solutions for a class of first-order neutral difference equations modelling physiological processes and conditions. Our approach is based on a fixed point theorem in cones as well as some analysis techniques.

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