scholarly journals Almost Periodic Functions on Time Scales and Applications

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Yongkun Li ◽  
Chao Wang
Keyword(s):  
Time Scales ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Mathematical Methods ◽  
Variable Delays ◽  
Definition Of ◽  
Almost Periodic Time Scales

We first propose the concept of almost periodic time scales and then give the definition of almost periodic functions on almost periodic time scales, then by using the theory of calculus on time scales and some mathematical methods, some basic results about almost periodic differential equations on almost periodic time scales are established. Based on these results, a class of high-order Hopfield neural networks with variable delays are studied on almost periodic time scales, and some sufficient conditions are established for the existence and global asymptotic stability of the almost periodic solution. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.

scholarly journals Almost Periodic Time Scales and Almost Periodic Functions on Time Scales

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Yongkun Li ◽  
Bing Li
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Basic Properties ◽  
New Concepts ◽  
Almost Periodic Time Scales

We propose some new concepts of almost periodic time scales and almost periodic functions on time scales and give some basic properties of these new types of almost periodic time scales and almost periodic functions on time scales. We also give some comments on a recent paper by Wang and Agarwal (2014) concerning a new almost periodic time scale.

scholarly journals Uniformly Almost Periodic Functions and Almost Periodic Solutions to Dynamic Equations on Time Scales

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
Yongkun Li ◽  
Chao Wang
Keyword(s):  
Periodic Solutions ◽  
Time Scales ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Periodic Sequences ◽  
Nonlinear Dynamic Equations ◽  
Definition Of

Firstly, we propose a concept of uniformly almost periodic functions on almost periodic time scales and investigate some basic properties of them. When time scaleT=ℝorℤ, our definition of the uniformly almost periodic functions is equivalent to the classical definitions of uniformly almost periodic functions and the uniformly almost periodic sequences, respectively. Then, based on these, we study the existence and uniqueness of almost periodic solutions and derive some fundamental conditions of admitting an exponential dichotomy to linear dynamic equations. Finally, as an application of our results, we study the existence of almost periodic solutions for an almost periodic nonlinear dynamic equations on time scales.

scholarly journals Cn-Almost Periodic Functions and an Application to a Lasota-Wazewska Model on Time Scales

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Li Yang ◽  
Yongkun Li ◽  
Wanqin Wu
Keyword(s):  
Time Scales ◽  
Differential Inequality ◽  
Global Exponential Stability ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Inequality Techniques

We first give the definition and some properties ofCn-almost periodic functions on time scales. Then, as an application, we are concerned with a class of Lasota-Wazewska models on time scales. By means of the fixed point theory and differential inequality techniques on time scales, we obtain some sufficient conditions ensuring the existence and global exponential stability ofC1-almost periodic solutions for the considered model. Our results are essentially new whenT=RorT=Z. Finally, we present a numerical example to show the feasibility of obtained results.

scholarly journals Permanence and Almost Periodic Solution for an Enterprise Cluster Model Based on Ecology Theory with Feedback Controls on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Yuanhong Zhi ◽  
Zunling Ding ◽  
Yongkun Li
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Cluster Model ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Asymptotically Stable ◽  
Almost Periodic ◽  
Feedback Controls ◽  
Competition And Cooperation ◽  
Enterprise Cluster

We present a model with feedback controls based on ecology theory, which effectively describes the competition and cooperation of enterprise cluster in real economic environments. Applying the comparison theorem of dynamic equations on time scales and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and the existence of uniformly asymptotically stable almost periodic solution of the system are obtained.

Semidirect Product Compactifications

1983 ◽  
Vol 35 (1) ◽  
pp. 1-32
Author(s):  
F. Dangello ◽  
R. Lindahl
Keyword(s):  
Direct Product ◽  
Semidirect Product ◽  
Topological Semigroup ◽  
Sufficient Conditions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Semigroups ◽  
Weakly Almost Periodic ◽  
Necessary And Sufficient

1. Introduction. K. Deleeuw and I. Glicksberg [4] proved that if S and T are commutative topological semigroups with identity, then the Bochner almost periodic compactification of S × T is the direct product of the Bochner almost periodic compactifications of S and T. In Section 3 we consider the semidirect product of two semi topological semigroups with identity and two unital C*-subalgebras and of W(S) and W(T) respectively, where W(S) is the weakly almost periodic functions on S. We obtain necessary and sufficient conditions and for a semidirect product compactification of to exist such that this compactification is a semi topological semigroup and such that this compactification is a topological semigroup. Moreover, we obtain the largest such compactifications.

scholarly journals Almost Periodic Solutions for Second Order Dynamic Equations on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yan Wang ◽  
Lan Li
Keyword(s):  
Fixed Point ◽  
Periodic Solutions ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Second Order ◽  
Almost Periodic Functions ◽  
Dynamic Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions

We firstly introduce the concept and the properties ofCmalmost periodic functions on time scales, which generalizes the concept of almost periodic functions on time scales and the concept ofC(n)-almost periodic functions. Secondly, we consider the existence and uniqueness of almost periodic solutions for second order dynamic equations on time scales by Schauder’s fixed point theorem and contracting mapping principle. At last, we obtain alternative theorems for second order dynamic equations on time scales.

scholarly journals Almost Periodic Solutions to Dynamic Equations on Time Scales and Applications

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Yongkun Li ◽  
Chao Wang
Keyword(s):  
Periodic Solution ◽  
Time Scales ◽  
Existence And Uniqueness ◽  
Exponential Dichotomy ◽  
Sufficient Conditions ◽  
Almost Periodic Solution ◽  
Dynamic Equations ◽  
Almost Periodic ◽  
Linear Dynamic ◽  
Expression Form

We first introduce the concept of admitting an exponential dichotomy to a class of linear dynamic equations on time scales and study the existence and uniqueness of almost periodic solution and its expression form to this class of linear dynamic equations on time scales. Then, as an application, using these concepts and results, we establish sufficient conditions for the existence and exponential stability of almost periodic solution to a class of Hopfield neural networks with delays. Finally, two examples and numerical simulations given to illustrate our results are plausible and meaningful.

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