Work

Dynamical Analysis of Fractional-Order Quaternion-Valued Neural Networks with Leakage and Communication Delays

Year: 2025

Type: article

Abstract: This paper investigates the stability and Hopf bifurcation problems of fractional-order quaternion-valued neural networks (FOQVNNs) with leakage delay and communication delay. Utilizing the Hamilton rule of quaternions, the fractional-order quaternion-valued time-delay neural network model is transformed into an equivalent fractional-order real-valued time-delay neural network system. Then, employing the stability theory and bifurcation theory of fractional-order dynamical systems, novel sufficient criteria are derived to ensure system stability and to induce Hopf bifurcation, respectively, using the leakage delay and the communication delay as bifurcation parameters. Furthermore, the influences of both delay types on the bifurcation behavior of FOQVNNs are analyzed in depth. To verify the correctness of the theoretical results, bifurcation diagrams and simulation results generated using MATLAB are presented. The theoretical results established in this paper provide a significant theoretical basis for the analysis and design of FOQVNNs.

Source: Fractal and Fractional

DOI: 10.3390/fractalfract9090559

Authors: Qiankun Wang, Tianzeng Li, Yu Wang, Xiaowen Tan

Institutions: Sichuan University of Science and Engineering, Hainan Normal University

Language: English

Topic: Neural Networks Stability and Synchronization

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,258

Funders: Hainan Normal University, Sichuan University of Science and Engineering, Sichuan University