Mathematical study on bifurcation dynamics and control mechanism of tri‐neuron bidirectional associative memory neural networks including delay

• Published in: Mathematical methods in the applied sciences Vol. 48; no. 7; pp. 7820 - 7844
• Main Authors: Ou, Wei, Xu, Changjin, Cui, Qingyi, Liu, Zixin, Pang, Yicheng, Farman, Muhammad, Ahmad, Shabir, Zeb, Anwar
• Format: Journal Article
• Language: English
• Published: Freiburg Wiley Subscription Services, Inc 15.05.2025
• Subjects: Associative memory; BAM neural networks; Delay; Dynamic models; Fixed points (mathematics); Hopf bifurcation; hybrid controller; Neural networks; peculiarity of solution; Recurrent neural networks; Simulation; stability; Stability criteria
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.9347

Applying delayed dynamical models to characterize the dynamics of neural networks has attracted great interest from scientific community. In this current manuscript, a kind of new tri‐neuron bidirectional associative memory (BAM) neural networks including delay are formulated. The properties of solution and Hopf bifurcation issue of the established tri‐neuron BAM neural networks including delay are investigated. First, we check the existence and uniqueness of the solution to the formulated delayed tri‐neuron BAM neural networks by virtue of fixed point theorem. Second, we seek the boundedness of the solution of the formulated delayed tri‐neuron BAM neural networks in view of a suitable function and inequality skills. Third, the delay‐independent criteria on stability and bifurcation of the formulated delayed tri‐neuron BAM neural networks are acquired. Fourth, Hopf bifurcation control aspect of the formulated delayed tri‐neuron BAM neural networks is explored via designing two proper hybrid controllers. To prove the accuracy of gained primary assertions, software simulation experiments are put into practice.