Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks

Marat Akhmet, Madina Tleubergenova and Zakhira Nugayeva
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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
Zakhira Nugayeva: Department of Mathematics, Aktobe Regional State University, Aktobe 030000, Kazakhstan

Mathematics, 2020, vol. 8, issue 10, 1-14

Abstract: In this paper, unpredictable oscillations in Hopfield-type neural networks is under investigation. The motion strongly relates to Poincaré chaos. Thus, the importance of the dynamics is indisputable for those problems of artificial intelligence, brain activity and robotics, which rely on chaos. Sufficient conditions for the existence and uniqueness of exponentially stable unpredictable solutions are determined. The oscillations continue the line of periodic and almost periodic motions, which already are verified as effective instruments of analysis and applications for image recognition, information processing and other areas of neuroscience. The concept of strongly unpredictable oscillations is a significant novelty of the present research, since the presence of chaos in each coordinate of the space state provides new opportunities in applications. Additionally to the theoretical analysis, we have provided strong simulation arguments, considering that all of the assumed conditions are fulfilled.

Keywords: Hopfield-type neural networks; Poincaré chaos; strongly unpredictable oscillations; asymptotic stability; numerical simulations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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