https://doi.org/10.1140/epjp/s13360-025-06042-4
Regular Article
Elegant homogeneous basin of attraction in two-memristor cyclic Hopfield neural network
1
School of Design and Innovation, Changzhou Vocational Institute of Mechatronic Technology, 213164, Changzhou, China
2
Wang Zheng School of Microelectronics, Changzhou University, 213159, Changzhou, China
Received:
23
October
2024
Accepted:
18
January
2025
Published online:
4
February
2025
It has been proved that the conventional cyclic Hopfield neural network (CHNN) with three neurons does not exhibit chaotic kinetics. Recently, a memristive CHNN has been developed to generate chaos by replacing two self-connected resistive weights with two memristor adaptive weights. Can two memristor adaptive weights replace the resistive weights of one self-feedback connection and one coupling connection, respectively? In this study, a two-memristor CHNN (TM-CHNN) is presented to generate chaos and planar homogeneous coexisting attractors. TM-CHNN owns a planar equilibrium set, and its stability is periodically distributed over the two memristor’s initial state plane. Using numerical measures, the bifurcation kinetics and typical attractors are revealed, and the planar homogeneous coexisting attractors boosted by memristor’s initial states and kinetic effects caused by non-memristor’s initial states are studied. The numerical results show that TM-CHNN can exhibit chaotic kinetics, especially produce planar homogeneous three-scroll chaotic and multi-periodic attractors, whose elegant homogeneous basins of attraction have exquisite manifold structures and fractal boundaries, and have complex evolution with the change of the memristor’s initial states and non-memristor’s initial states. Additionally, FPGA hardware device is made for implementing TM-CHNN and planar homogeneous coexisting attractors are acquired experimentally to verify the simulated results.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
