| Citation: |
Yongkun Li, Xiaoli Huang. WEYL ALMOST PERIODIC FUNCTIONS ON TIME SCALES AND WEYL ALMOST PERIODIC SOLUTIONS OF DYNAMIC EQUATIONS WITH DELAYS[J]. Journal of Applied Analysis & Computation, 2022, 12(3): 1022-1042. doi: 10.11948/20220102
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WEYL ALMOST PERIODIC FUNCTIONS ON TIME SCALES AND WEYL ALMOST PERIODIC SOLUTIONS OF DYNAMIC EQUATIONS WITH DELAYS
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Abstract
Due to the incompleteness of the space composed of Weyl almost periodic functions, there are few results on the existence of Weyl almost periodic solutions of differential equations. In addition, as a discrete analogs of differential equations, there is almost no result of the existence of Weyl almost periodic solutions of difference equations. Because dynamic equations on time scales can unify the study of differential equations and difference equations. Therefore, in this paper, we first propose a concept of Weyl almost periodic functions on time scales. Then, taking a Clifford-valued neural network with time-varying delays on time scales as an example of dynamic equations on time scales, we study the existence and stability of Weyl almost periodic solutions of this neural network on time scales. Even when the system we consider degenerates into a real-valued system, our results are new. A numerical example is given to illustrate the feasibility of our results.
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References
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Yongkun Li, Xiaoli Huang. WEYL ALMOST PERIODIC FUNCTIONS ON TIME SCALES AND WEYL ALMOST PERIODIC SOLUTIONS OF DYNAMIC EQUATIONS WITH DELAYS[J]. Journal of Applied Analysis & Computation, 2022, 12(3): 1022-1042. doi: 10.11948/20220102
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Figure 1.
$ \mathbb{T}=\mathbb{R} $ , states$ x^l_1(t) $ and$ x^l_2(t) $ of system (1.1) with different initial values. -
Figure 2.
$ \mathbb{T}=\mathbb{Z} $ , states$ x^l_1(t) $ and$ x^l_2(t) $ of system (1.1) with different initial values. -
Figure 3.
$ \mathbb{T}=\mathbb{R} $ , the global exponential stability of states$ x_1^0(t), x_1^1(t), x_1^2(t) $ and$ x_1^{12}(t) $ of system (1.1) with different initial values. -
Figure 4.
$ \mathbb{T}=\mathbb{R} $ , the global exponential stability of states$ x_2^0(t), x_2^1(t), x_2^2(t) $ and$ x_2^{12}(t) $ of system (1.1) with different initial values. -
Figure 5.
$ \mathbb{T}=\mathbb{Z} $ , the global exponential stability of states$ x_1^0(t), x_1^1(t), x_1^2(t) $ and$ x_1^{12}(t) $ of system (1.1) with different initial values. -
Figure 6.
$ \mathbb{T}=\mathbb{Z} $ , the global exponential stability of states$ x_2^0(t), x_2^1(t), x_2^2(t) $ and$ x_2^{12}(t) $ of system (1.1) with different initial values.