Strongly Unpredictable Oscillations of Hopfield-Type Neural Networks

AKHMET M., Tleubergenova M., Nugayeva Z.

MATHEMATICS, cilt.8, sa.10, ss.1-14, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 8 Sayı: 10
  • Basım Tarihi: 2020
  • Doi Numarası: 10.3390/math8101791
  • Dergi Adı: MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Communication Abstracts, Metadex, zbMATH, Directory of Open Access Journals, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1-14
  • Anahtar Kelimeler: Hopfield-type neural networks, Poincar&#233, chaos, strongly unpredictable oscillations, asymptotic stability, numerical simulations, ASSOCIATIVE MEMORY, CONVERGENCE RATE, POINCARE CHAOS, ATTRACTION, EQUATIONS, DOMAIN, SYNCHRONIZATION, SEGMENTATION, STABILITY
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, unpredictable oscillations in Hopfield-type neural networks is under investigation. The motion strongly relates to Poincare 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.