Chaos, Hyperchaos and Transient Chaos in a 4D Hopfield Neural Network: Numerical Analyses and PSpice Implementation

Victor Kamdoum Tamba, Gaetant Ngoko, Viet-Thanh Pham () and Giuseppe Grassi
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Victor Kamdoum Tamba: Department of Telecommunication and Network Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, Bandjoun P.O. Box 134, Cameroon
Gaetant Ngoko: Research Unit of Automation and Applied Computer, Department of Electrical Engineering, IUT-Fotso Victor of Bandjoun, University of Dschang, Bandjoun P.O. Box 134, Cameroon
Viet-Thanh Pham: Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City 70000, Vietnam
Giuseppe Grassi: Dipartimento Ingegneria Innovazione, Universita del Salento, 73100 Lecce, Italy

Mathematics, 2025, vol. 13, issue 11, 1-13

Abstract: The human brain is an extremely sophisticated system. Several neural models have been proposed to mimic and understand brain function. Most of them incorporate memristors to simulate autapse or self-coupling, electromagnetic radiation and the synaptic weight of the neuron. This article introduces and studies the dynamics of a Hopfield neural network (HNN) consisting of four neurons, where one of the synaptic weights of the neuron is replaced by a memristor. Theoretical aspects such as dissipation, the requirements for the existence of attractors, symmetry, equilibrium states and stability are studied. Numerical investigations of the model reveal that it develops very rich and diverse behaviors such as chaos, hyperchaos and transient chaos. These results obtained numerically are further supported by the results obtained from an electronic circuit of the system, constructed and simulated in PSpice. Both approaches show good agreement. In light of the findings from the numerical and experimental studies, it appears that the 4D Hopfield neural network under consideration in this work is more complex than its original version, which did not include a memristor.

Keywords: 4D Hopfield neural network; theoretical analyses; numerical investigations; complicated behaviors; analog circuit implementation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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