title: A comparative study of two modeling approaches in neural networks.
abstract: The neuron state modeling and the local field modeling provides two fundamental modeling approaches to neural network research, based on which a neural network system can be called either as a static neural network model or as a local field neural network model. These two models are theoretically compared in terms of their trajectory transformation property, equilibrium correspondence property, nontrivial attractive manifold property, global convergence as well as stability in many different senses. The comparison reveals an important stability invariance property of the two models in the sense that the stability (in any sense) of the static model is equivalent to that of a subsystem deduced from the local field model when restricted to a specific manifold. Such stability invariance property lays a sound theoretical foundation of validity of a useful, cross-fertilization type stability analysis methodology for various neural network models.
authors.affiliation: Institute for Information and System Sciences, Xi'an Jiaotong University, Xi'an, China. zbxu@mail.xjtu.edu.cn
authors.forename: Zong-Ben
authors.initials: ZB
authors.lastname: Xu
authors.forename: Hong
authors.initials: H
authors.lastname: Qiao
authors.forename: Jigen
authors.initials: J
authors.lastname: Peng
authors.forename: Bo
authors.initials: B
authors.lastname: Zhang
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D003198:Computer Simulation; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D017711:Nonlinear Dynamics