https://doi.org/10.1140/epjp/s13360-025-06914-9
Regular Article
Regular periodic cascades, chirality, and multistability in a memristive coupled heterogeneous neuron system
1
School of Electronic and Information Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, China
2
School of Mechatronic Engineering, Lanzhou Jiaotong University, 730070, Lanzhou, China
3
Engineering Department, University of Exeter, EX4 4QF, Exeter, UK
a
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Received:
17
June
2025
Accepted:
28
September
2025
Published online:
14
October
2025
Abstract
Exploring the dynamics of heterogeneous neural networks holds significant practical value in understanding the operational principles of complex neuron systems. This paper studies the dynamic behavior transition in a memristor-coupled heterogeneous neuron system through a combination of theoretical analysis and numerical simulation. A heterogeneous neuron system is constructed by coupling a continuous Rulkov neuron and a two-dimensional Hindmarsh-Rose (HR) neuron via a sinusoidally characterized memristor. Equilibrium analysis reveals that the system lacks equilibrium points but can generate hidden attractors. Several analytical tools, including single-parameter bifurcation diagrams, two-parameter periodic region diagrams, phase portraits, time series, and basins of attraction, are used to examine the system’s firing patterns. These analyses uncover numerous self-similar “shrimp-shaped” structures. Notably, under varying coupling strengths, the system exhibits complex bifurcation patterns, including regular adding-doubling cascades with distinct non-quantum chirality. The system also demonstrates remarkable initial condition sensitivity, with coexisting homogeneous firing patterns and multistability. Finally, an analog equivalent circuit is implemented to validate the numerical 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.
