Spatiotemporal dynamic of a coupled neutral-type neural network with time delay and diffusion
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ORIGINAL ARTICLE
Spatiotemporal dynamic of a coupled neutral-type neural network with time delay and diffusion Wenjie Hu1,2 • Xing Qiao2 • Tao Dong2 Received: 21 July 2019 / Accepted: 29 September 2020 Ó Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In this paper, a delayed neutral-type neural network with diffusion is considered. Three spatiotemporal dynamic problems of such network, i.e., stability, Turing instability and oscillation, are addressed in detail. It is found that the diffusion may lead to Turing instability, and the time delay may result in oscillation. Then, a novel computing method is proposed to investigate the oscillation properties. Finally, numerical results not only verify the obtained results but also show the diffusion coefficients have a great effect on the appearance of pattern. There are six spatiotemporal patterns when diffusion varying. Keywords Neutral-type Turing instability Oscillation Stability Reaction diffusion
1 Introduction Recently, many researchers embark on research into the neutral-type neural network (NTNN) because it presents the excellent performance in various data applications such as semantic analysis, sequence learning, data classification and so on [1–4]. The successful reason of NTNN is that it can store more past state information than other neural networks. Many engineering applications of NTNN are based on its dynamic behaviors, i.e., the associate memory is based on the stability of NTNN’s equilibrium. As is known to all, time delay widely exits in the NTNN because neuron needs time to store, process and transmit the state & Tao Dong [email protected] Wenjie Hu [email protected] Xing Qiao [email protected] 1
Research Center for Enterprise Management, School of Business Administration, Chongqing Technology and Business University, Chongqing 400067, People’s Republic of China
2
Chongqing Key Laboratory of Nonlinear Circuits and Intelligent Information Processing, College of Electronics and Information Engineering, Southwest University, Chongqing 400715, People’s Republic of China
information. NTNN with time delay exhibits complicated dynamic behaviors such as periodic solution, quasi periodic solution, homoclinic solution, heteroclinic solution. Therefore, there are many works on the dynamic of delayed NTNN [5–14]. In neural system, neurons interact with each other through the diffusion of neuronal cytoplasm. Experiments show that the diffusion of neuronal cytoplasm may lead to the spatiotemporal dynamic of neural network changing. Thus, studying the spatiotemporal dynamic behaviors of neural networks with diffusion becomes a hot topic. Up to date, many important results have been arrived on this research topic [15–23]. The Hopf bifurcation condition for reaction diffusion the Cohen–Grossberg neural network, Hopfield neural network and neural oscillator is investigated [15–21]. In [22–24], the equilibrium properties and dynamic behaviors for the Hopfield neural network the Cohen
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