Dynamics of Shunting Inhibitory Cellular Neural Networks with Variable Two-Component Passive Decay Rates and Poisson Stable Inputs


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AKHMET M., Tleubergenova M., Zhamanshin A.

Symmetry, vol.14, no.6, 2022 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.3390/sym14061162
  • Journal Name: Symmetry
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, INSPEC, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Keywords: shunting inhibitory cellular neural networks, compartmental passive decay rate, Poisson stable inputs, outputs and rates, the method of included intervals, asymptotic stability of outputs, ALMOST-PERIODIC SOLUTIONS, ANTIPERIODIC SOLUTIONS, POINCARE CHAOS, RECURRENT, STABILITY, SYSTEMS

Abstract

© 2022 by the authors. Licensee MDPI, Basel, Switzerland.Shunting inhibitory cellular neural networks with continuous time-varying rates and inputs are the focus of this research. A new model is considered with compartmental passive decay rates which consist of periodic and Poisson stable components. The first component guarantees the Poisson stability of the dynamics, and the second one causes irregular oscillations. The inputs are Poisson stable to take into account the more sophisticated environment of the networks. The rates and inputs are synchronized to obtain Poisson stable outputs. A new efficient technique for checking the recurrence, the method of included intervals, is applied. Sufficient conditions for the existence of a Poisson stable solution and its asymptotic stability were obtained. Numerical simulations of Poisson stable outputs as well as inputs are provided. Examples of the model with Poisson stable rates, inputs and outputs confirm the feasibility of theoretical results. Discussions were undertaken to provide additional light on the relation of the obtained results with practical and theoretical potentials of neuroscience. Quantitative characteristics are suggested, which can be useful for the future applications of the results. In particular, the center of antisymmetry for the degree of periodicity is determined.