In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabili...In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.展开更多
In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transf...In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.展开更多
基金supported by Social Science Fund of Hunan province(Grant No.22JD074)the Research Foundation of Education Bureau of Hunan province(Grant No.22B0912).
文摘In this paper, a class of discontinuous neutral-type neural networks (NTNNs) with proportional delays is considered. The targets of the paper are to study the problem of periodic solutions and fixed-time (FXT) stabilization of the addressed neural networks. In order to complete the targets, based on set-valued map, differential inclusions theory, coincidence theorem and Hölder inequality technique, some new proportional delay-dependent criteria shown by the inequalities are derived. Based on the fact of the existence of solution, further by applying the FXT stability lemmas and equivalent transformation, the zero solution of closed-loop system achieves FXT stabilization and the corresponding settling-times are estimated. Some previous related works on NTNNs are extended. Finally, one typical example is provided to show the effectiveness of the established results.
文摘In this paper, a characterization of almost periodicity of topological transformation groups on uniform spaces is given. By searching the appropriate base for uniform structure, it is shown that the topological transformation group is topologically equivalent to an isometric one if it is uniformly equicontinuous.
