Almost periodicity of set-valued functions and set dynamic equations on time scales

Hong, Soon-Sam; Peng, Yuxin

doi:10.1016/j.ins.2015.10.008

Cited by 18 publications

(15 citation statements)

References 35 publications

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“…Finally, under the assumption of the exponential dichotomy, the zero solution of the linear homogeneous set dynamic equation Δ ( ) = ( ) ( ) is the unique solution that is bounded in T + (see, e.g., [42,Lemma 4.13]). Let 1 , 2 both be the solutions of ISDE (59).…”

Section: (69)mentioning

confidence: 99%

Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

Hong

Gao

Peng

2014

Abstract and Applied Analysis

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A class of new nonlinear impulsive set dynamic equations is considered based on a new generalized derivative of set-valued functions developed on time scales in this paper. Some novel criteria are established for the existence and stability of solutions of such model. The approaches generalize and incorporate as special cases many known results for set (or fuzzy) differential equations and difference equations when the time scale is the set of the real numbers or the integers, respectively. Finally, some examples show the applicability of our results.

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Section: (69)mentioning

confidence: 99%

Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

Hong

Gao

Peng

2014

Abstract and Applied Analysis

Self Cite

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“…On the other hand, in order to study the almost periodicity on time scales, a concept of almost periodic time scales was proposed in [8]. Based on this concept, a series of concepts of almost periodic function classes, such as almost periodic functions [8], pseudo almost periodic functions [9], almost automorphic functions [10], weighted pseudo almost automorphic functions [11], almost periodic set-valued functions [12], almost periodic functions in the sense of Stepanov on time scales [13] and so on were defined successively. Although the concept of almost periodic time scales in [8] can unify the continuous and discrete situations effectively, it is very restrictive because it requires the time scale with certain global additivity.…”

Section: Introductionmentioning

confidence: 99%

Almost Periodic Functions on the Quantum Time Scale and Applications

2019

Discrete Dynamics in Nature and Society

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In this paper, we first propose two types of concepts of almost periodic functions on the quantum time scale. Secondly, we study some basic properties of almost periodic functions on the quantum time scale. Thirdly, based on these, we obtain a result about the existence and uniqueness of almost periodic solutions of dynamic equations on the quantum time scale by Lyapunov method. Then, we give a equivalent definition of almost periodic functions on the quantum time scale. Finally, as an application, we propose a class of high-order Hopfield neural networks on the quantum time scale and establish the existence of almost periodic solutions of this class of neural networks.

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“…On the other hand, in order to study the almost periodic dynamic equations on time scales, a concept of almost periodic time scales was proposed in [27]. Based on this concept, almost periodic functions [27], pseudo almost periodic functions [28], almost automorphic functions [29], weighted pseudo almost automorphic functions [30], almost periodic set-valued functions [31], almost periodic functions in the sense of Stepanov on time scales [32] and so on were defined successively. Also, some works have been done under the concept of almost periodic time scales (see [33,34,35,36,37,38,39,40]).…”

Section: Introductionmentioning

confidence: 99%

The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

Meng

2019

Mathematics

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In this paper, a class of neutral type competitive neural networks with mixed timevarying delays and leakage delays on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed point theorem and the theory of calculus on time scales, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions for this class of neural networks. The obtained results are completely new and indicate that both the continuous time and the discrete time cases of the networks share the same dynamical behavior. Finally, an examples is given to show the effectiveness of the obtained results.

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Almost periodicity of set-valued functions and set dynamic equations on time scales

Cited by 18 publications

References 35 publications

Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

Solvability and Stability of Impulsive Set Dynamic Equations on Time Scales

Almost Periodic Functions on the Quantum Time Scale and Applications

The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

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