Domain-Structured Chaos in a Hopfield Neural Network

AKHMET M., Alejaily E. M.

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, cilt.29, sa.14, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 29 Sayı: 14
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1142/s0218127419502055
  • Dergi Adı: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: Hopfield neural network, domain-structured chaos, higher-dimensional chaos, SYSTEMS
  • Orta Doğu Teknik Üniversitesi Adresli: Evet

Özet

In this paper, we provide a new method for constructing chaotic Hopfield neural networks. Our approach is based on structuring the domain to form a special set through the discrete evolution of the network state variables. In the chaotic regime, the formed set is invariant under the system governing the dynamics of the neural network. The approach can be viewed as an extension of the unimodality technique for one-dimensional map, thereby generating chaos from higher-dimensional systems. We show that the discrete Hopfield neural network considered is chaotic in the sense of Devaney, Li-Yorke, and Poincare. Mathematical analysis and numerical simulation are provided to confirm the presence of chaos in the network.