Bifurcation Phenomenon and Control Technique in Fractional BAM Neural Network Models Concerning Delays

• Published in: Fractal and fractional 2023-01, Vol.7 (1), p.7
• Main Authors: Li, Peiluan, Lu, Yuejing, Xu, Changjin, Ren, Jing
• Format: Article
• Language: English
• Subjects: delayed feedback controller; Dynamic stability; Feedback control; fractional BAM neural network models; Hopf bifurcation; Investigations; Lipschitz condition; Neural networks; peculiarity of solution; Recurrent neural networks; stability; Stability criteria
• ISSN: 2504-3110; 2504-3110
• DOI: 10.3390/fractalfract7010007

In this current study, we formulate a kind of new fractional BAM neural network model concerning five neurons and time delays. First, we explore the existence and uniqueness of the solution of the formulated fractional delay BAM neural network models via the Lipschitz condition. Second, we study the boundedness of the solution to the formulated fractional delayed BAM neural network models using a proper function. Third, we set up a novel sufficient criterion on the onset of the Hopf bifurcation stability of the formulated fractional BAM neural network models by virtue of the stability criterion and bifurcation principle of fractional delayed dynamical systems. Fourth, a delayed feedback controller is applied to command the time of occurrence of the bifurcation and stability domain of the formulated fractional delayed BAM neural network models. Lastly, software simulation figures are provided to verify the key outcomes. The theoretical outcomes obtained through this exploration can play a vital role in controlling and devising networks.