Quasi-pinning synchronization and stabilization of fractional order BAM neural networks with delays and discontinuous neuron activations

A. Pratap, R. Raja, J. Cao, Fathalla A. Rihan, Aly R. Seadawy

Research output: Contribution to journalArticlepeer-review

35 Citations (Scopus)

Abstract

This manuscript concerns quasi-pinning synchronization and β-exponential pinning stabilization for a class of fractional order BAM neural networks with time-varying delays and discontinuous neuron activations (FBAMNNDDAs). Firstly, under the framework of Filippov solution and fractional-order differential inclusions analysis for the initial value problem of FBAMNNDDAs is presented. Secondly, two kinds of novel pinning controllers according to pinning control technique are designed. By means of fractional order Lyapunov method and designed pinning control strategy, the sufficient criteria is given first to ensure the quasi-synchronization for the dynamic behavior of FBAMNNDDAs. Furthermore, the error bound of pinning synchronization is explicitly evaluated. Thirdly, via Kakutani s fixed point theorem of set-valued map analysis, Razumikhin condition, and a nonlinear pinning controller, the existence and β-exponential stabilization of FBAMNNDDAs equilibrium point is obtained in the voice of linear matrix inequality (LMI) technique. Fourthly, based on as well as Mittag-Leffler function and growth condition, the global existence of a solution in the Filippov sense of such system is guaranteed with detailed proof. At last, a numerical example with computer simulations are performed to illustrate the effectiveness of proposed theoretical consequences.

Original languageEnglish
Article number109491
JournalChaos, Solitons and Fractals
DOIs
Publication statusAccepted/In press - Jan 1 2019

Keywords

  • Discontinuous BAM-type neural networks
  • Filippov's solutions
  • Fractional order
  • Pinning control
  • Quasi-synchronization
  • Time-varying delays
  • β-Exponential stabilization

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

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