Poisson Stability in Symmetrical Impulsive Shunting Inhibitory Cellular Neural Networks with Generalized Piecewise Constant Argument

被引:5
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, Turkey
[2] Aktobe Reg Univ, Dept Math, Aktobe 030000, Kazakhstan
[3] Inst Informat & Computat Technol CS MES RK, Alma Ata 050010, Kazakhstan
来源
SYMMETRY-BASEL | 2022年 / 14卷 / 09期
关键词
impulsive shunting inhibitory cellular neural networks; symmetry of impulsive and differential parts; continuous and impact activations; generalized piecewise constant argument; method of included intervals; continuous and discontinuous Poisson stable inputs and outputs; GLOBAL EXPONENTIAL STABILITY; ALMOST-PERIODIC SOLUTIONS; DIFFERENTIAL-EQUATIONS; NEGATIVE CAPACITANCE; EXISTENCE;
D O I
10.3390/sym14091754
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
In the paper, shunting inhibitory cellular neural networks with impulses and the generalized piecewise constant argument are under discussion. The main modeling novelty is that the impulsive part of the systems is symmetrical to the differential part. Moreover, the model depends not only on the continuous time, but also the generalized piecewise constant argument. The process is subdued to Poisson stable inputs, which cause the new type of recurrent signals. The method of included intervals, recently introduced approach of recurrent motions checking, is effectively utilized. The existence and asymptotic properties of the unique Poisson stable motion are investigated. Simulation examples for results are provided. Finally, comparing impulsive shunting inhibitory cellular neural networks with former neural network models, we discuss the significance of the components of our model.
引用
收藏
页数:22
相关论文
共 51 条
[1]   Continuous-time additive Hopfield-type neural networks with impulses [J].
Akça, H ;
Alassar, R ;
Covachev, V ;
Covacheva, Z ;
Al-Zahrani, E .
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2004, 290 (02) :436-451
[2]  
Akhmet M., 2022, DISCONTIN NONLINEARI, V11, P373, DOI [10.5890/DNC.2022.09.001, DOI 10.5890/DNC.2022.09.001]
[3]  
Akhmet M, 2021, Domain structured dynamics: Unpredictability, chaos, randomness, fractals, differential equations and neural networks
[4]  
Akhmet M., 2010, Principles of Discontinuous Dynamical Systems, DOI DOI 10.1007/978-1-4419-6581-3
[5]  
Akhmet M., 2022, DISCONTIN NONLINEAR, V11, P73
[6]  
Akhmet M, 2020, Almost Periodicity, Chaos, and Asymptotic Equivalence
[7]   Integral manifolds of differential equations with piecewise constant argument of generalized type [J].
Akhmet, M. U. .
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (02) :367-383
[8]  
Akhmet M.U., 2005, P C DIFF DIFF EQ FLO, P11
[9]   Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs [J].
Akhmet, Marat ;
Tleubergenova, Madina ;
Zhamanshin, Akylbek .
SYMMETRY-BASEL, 2022, 14 (06)
[10]   Modulo Periodic Poisson Stable Solutions of Quasilinear Differential Equations [J].
Akhmet, Marat ;
Tleubergenova, Madina ;
Zhamanshin, Akylbek .
ENTROPY, 2021, 23 (11)