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


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AKHMET M., Tleubergenova M., Seilova R., Nugayeva Z.

SYMMETRY-BASEL, vol.14, no.9, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 9
  • Publication Date: 2022
  • Doi Number: 10.3390/sym14091754
  • Journal Name: SYMMETRY-BASEL
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: 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
  • Middle East Technical University Affiliated: Yes

Abstract

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.