Inertial Neural Networks with Unpredictable Oscillations

Marat Akhmet, Madina Tleubergenova and Akylbek Zhamanshin
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Marat Akhmet: Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey
Madina Tleubergenova: Department of Mathematics, Aktobe Regional State University, Aktobe 030000, Kazakhstan
Akylbek Zhamanshin: Department of Mathematics, Aktobe Regional State University, Aktobe 030000, Kazakhstan

Mathematics, 2020, vol. 8, issue 10, 1-11

Abstract: In this paper, inertial neural networks are under investigation, that is, the second order differential equations. The recently introduced new type of motions, unpredictable oscillations, are considered for the models. The motions continue a line of periodic and almost periodic oscillations. The research is of very strong importance for neuroscience, since the existence of unpredictable solutions proves Poincaré chaos. Sufficient conditions have been determined for the existence, uniqueness, and exponential stability of unpredictable solutions. The results can significantly extend the role of oscillations for artificial neural networks exploitation, since they provide strong new theoretical and practical opportunities for implementation of methods of chaos extension, synchronization, stabilization, and control of periodic motions in various types of neural networks. Numerical simulations are presented to demonstrate the validity of the theoretical results.

Keywords: inertial neural networks; unpredictable oscillations; asymptotic stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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