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Complicated Dynamics of a Delayed Photonic Reservoir Computing System

Lijun Pei

https://orcid.org/0000-0002-3767-5656

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, P. R. China

E-mail Address: peilijun@zzu.edu.cn

Corresponding author.

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and

Mengyu Zhang

School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, Henan, P. R. China

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https://doi.org/10.1142/S0218127422501152Cited by:2 (Source: Crossref)

Abstract

In this paper, we consider the complicated dynamics of a delay-based photonic reservoir computing system. Since conventional computer architectures are approaching their limit, it is imperative to find new, efficient and fast ways of data processing. Photonic reservoir computing (RC) is a promising way which combines the computational capabilities of recurrent neural networks with high processing speed and energy efficiency of photonics. As the RC system is very promising, we analyze its dynamics so that we can make better use of it. In this paper, we mainly focus on its double Hopf bifurcation. We first analyze the existence of double Hopf bifurcation points. Then we use DDE-BIFTOOL to draw the bifurcation diagrams with respect to two bifurcation parameters, i.e. feedback strength $η$ and delay $τ$ , and give a clear picture of the double Hopf bifurcation points of the system. These figures show stability switches and the existence of double Hopf bifurcation points. Finally, we employ the method of multiple scales to obtain their normal forms, use the method of normal form to unfold and classify their local dynamics. The classification and unfolding of these double Hopf bifurcation points are obtained. Three types of double Hopf bifurcations are found. We verify the results by numerical simulations and find its complicated behavioral dynamics. For example, there exist stable equilibrium, stable periodic and quasi-periodic solutions in distinct regions. The discovered rich dynamical phenomena can help us to choose suitable values of parameters to achieve excellent performance of RC.

This work was supported by the NNSF of China under the Grant Nos. 11972327 and 11372282.

Keywords:

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