https://doi.org/10.1140/epjs/s11734-025-01785-8
Regular Article
Advancing firing model design with cosine nonlinearity: slow variables from discrete memristors and their impact on complex electrical activities
1
School of Mechanical and Electrical Engineering, Guizhou Normal University, 550025, Guiyang, Guizhou, China
2
School of Automation and Electronic Information, Xiangtan University, 411105, Xiangtan, Hunan, China
Received:
22
May
2025
Accepted:
27
June
2025
Published online:
16
July
2025
At present, the design of discrete memristor chaotic systems, analysis of their dynamic characteristics, applications, and circuit implementation have become focal points. Meanwhile, the modulation of discrete neuronal spiking behaviors has not yet garnered sufficient academic attention. Designing discrete nonlinear systems capable of processing spiking signals holds significant application value. This study first explores the dynamic behaviors of the Cosine chaotic map and reveals that this system can generate neuron-like spiking behaviors. To further enhance this spiking mechanism, a two-dimensional discrete memristor-based Cosine map is designed using the fast-slow mechanism, where the Cosine map serves as the fast system, while the accumulation and summation within the discrete memristor provide slow-variable modulation over the fast-variable dynamics. Numerical simulation results demonstrate that both the Cosine chaotic map and the discrete memristor Cosine map can process spiking signals. However, due to the inherent nonlinearity of the system, which itself can generate spikes, the designed system is only suitable for processing high-density spiking signals. Finally, analog circuits for both systems are designed using the PSim software, and system phase diagrams under different resistance parameters are presented, revealing spiking behaviors in the circuit environment. This study integrates nonlinear system dynamic analysis methods with spiking mechanisms from the field of neuronal research, laying a foundation for the future design and analysis of discrete spiking models.
Copyright comment 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.
© The Author(s), under exclusive licence to EDP Sciences, 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.
