scholarly journals Unique Existence Theorem of Solution of Almost Periodic Differential Equations on Time Scales

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Meng Hu ◽  
Lili Wang
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Time Scales ◽  
Dynamic Systems ◽  
Matrix Theory ◽  
Almost Periodic ◽  
Unique Existence ◽  
Almost Periodic Time Scales

By using the theory of calculus on time scales andM-matrix theory, the unique existence theorem of solution of almost periodic differential equations on almost periodic time scales is established. The result can be used to a large of dynamic systems.

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 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 Periodicity, almost periodicity for time scales and related functions

2016 ◽  
Vol 3 (1) ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Almost Periodic Time Scales

AbstractIn this paper, we study almost periodic and changing-periodic time scales considered byWang and Agarwal in 2015. Some improvements of almost periodic time scales are made. Furthermore, we introduce a new concept of periodic time scales in which the invariance for a time scale is dependent on an translation direction. Also some new results on periodic and changing-periodic time scales are presented.

scholarly journals A Further Study of Almost Periodic Time Scales with Some Notes and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal
Keyword(s):  
Neural Networks ◽  
Time Scales ◽  
Dynamic Equations ◽  
Almost Periodicity ◽  
Almost Periodic Solutions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Cauchy Matrix ◽  
Nonlinear Dynamic Equations ◽  
Almost Periodic Time Scales

We introduce three equivalent concepts of almost periodic time scales as a further study of the corresponding concept proposed in Li and Wang (2011) and several examples of almost periodic time scales which are not periodic are provided. Furthermore, the concepts of almost periodic functions are redefined under the sense of this new timescale concept. Finally, almost periodicity of Cauchy matrix for dynamic equations is proved under these new definitions. Based on these results, the existence of almost periodic solutions to a class of nonlinear dynamic equations is investigated by the almost periodicity of Cauchy matrix on almost periodic time scales. Besides, as an application, we apply our results to a class of high-order Hopfield neural networks.

Almost periodic fuzzy multidimensional dynamic systems and applications on time scales

2022 ◽  
Vol 156 ◽  
pp. 111781
Author(s):  
Chao Wang ◽  
Ravi P. Agarwal ◽  
Donal O’Regan
Keyword(s):  
Time Scales ◽  
Dynamic Systems ◽  
Almost Periodic

scholarly journals Almost Automorphic Functions on the Quantum Time Scale and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yongkun Li
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Dynamic Equations ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Quantum Time ◽  
Almost Periodic Time Scales ◽  
Automorphic Functions ◽  
General Time

We first propose two types of concepts of almost automorphic functions on the quantum time scale. Secondly, we study some basic properties of almost automorphic functions on the quantum time scale. Then, we introduce a transformation between functions defined on the quantum time scale and functions defined on the set of generalized integer numbers; by using this transformation we give equivalent definitions of almost automorphic functions on the quantum time scale; following the idea of the transformation, we also give a concept of almost automorphic functions on more general time scales that can unify the concepts of almost automorphic functions on almost periodic time scales and on the quantum time scale. Finally, as an application of our results, we establish the existence of almost automorphic solutions of linear and semilinear dynamic equations on the quantum time scale.

Sign in / Sign up

Export Citation Format

Share Document