Overview of Bifurcation Dynamics in Neural Networks

Since the introduction of the renowned Hopfield neural network in 1982, the bifurcation dynamics of neural networks has garnered significant academic attention. Firstly, an overview of the mathematical models of four types of classical neural networks and their applications in various fields is provided. Subsequently, the research results on the bifurcation dynamics of integer-order neural networks (IONNs), fractional-order neural networks (FONNs), supernumerary-domain neural networks (SDNNs), and reaction-diffusion neural networks (RDNNs) in the past three decades are summarized. The effects of various combinations of factors, including node size, coupling, topology, system order, complex value, quaternion, octonion, diffusion, time delay, stochasticity, impulse, memristor, and activation function, on the bifurcation dynamics of neural networks are analyzed, and the wide applications of neural networks in various fields are also demonstrated. Finally, the challenges and potential research directions concerning neural network bifurcation dynamics are summarized and prospected. © 2025 Science Press. All rights reserved.