Symmetrical Impulsive Inertial Neural Networks with Unpredictable and Poisson-Stable Oscillations

被引:2
作者
Akhmet, Marat [1 ]
Tleubergenova, Madina [2 ,3 ]
Seilova, Roza [2 ,3 ]
Nugayeva, Zakhira [2 ,3 ]
机构
[1] Middle East Tech Univ, Dept Math, TR-06800 Ankara, Turkiye
[2] Aktobe Reg Univ, Dept Math, Aktobe 030000, Kazakhstan
[3] Inst Informat & Computat Technol CS MES RK, Alma Ata 050000, Kazakhstan
来源
SYMMETRY-BASEL | 2023年 / 15卷 / 10期
关键词
impulsive inertial neural networks; symmetry of differential and impulsive parts; unpredictable oscillations; Poisson-stable oscillations; unpredictable input-output; Poisson couple; the method of included intervals; Poincare chaos; exponential stability; STABILITY; DELAYS;
D O I
10.3390/sym15101812
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
This paper explores the novel concept of discontinuous unpredictable and Poisson-stable motions within impulsive inertial neural networks. The primary focus is on a specific neural network architecture where impulses mimic the structure of the original model, that is, continuous and discrete parts are symmetrical. This unique modeling decision aligns with the real-world behavior of systems, where voltage typically remains smooth and continuous but may exhibit sudden changes due to various factors such as switches, sudden loads, or faults. The paper introduces the representation of these abrupt voltage transitions as discontinuous derivatives, providing a more accurate depiction of real-world scenarios. Thus, the focus of the research is a model, exceptional in its generality. To study Poisson stability, the method of included intervals is extended for discontinuous functions and B-topology. The theoretical findings are substantiated with numerical examples, demonstrating the practical feasibility of the proposed model.
引用
收藏
页数:22
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