Rakkiyappan R, Velmurugan G, Cao J. Stability analysis of memristor-based fractional-order neural networks with different memductance functions.
Cogn Neurodyn 2015;
9:145-77. [PMID:
25861402 PMCID:
PMC4384520 DOI:
10.1007/s11571-014-9312-2]
[Citation(s) in RCA: 49] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/04/2014] [Revised: 09/03/2014] [Accepted: 09/08/2014] [Indexed: 11/26/2022] Open
Abstract
In this paper, the problem of the existence, uniqueness and uniform stability of memristor-based fractional-order neural networks (MFNNs) with two different types of memductance functions is extensively investigated. Moreover, we formulate the complex-valued memristor-based fractional-order neural networks (CVMFNNs) with two different types of memductance functions and analyze the existence, uniqueness and uniform stability of such networks. By using Banach contraction principle and analysis technique, some sufficient conditions are obtained to ensure the existence, uniqueness and uniform stability of the considered MFNNs and CVMFNNs with two different types of memductance functions. The analysis results establish from the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, four numerical examples are presented to show the effectiveness of our theoretical results.
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