title: The breaking of a delayed ring neural network contributes to stability: The rule and exceptions.
abstract: We prove that in our mathematical model the breaking of a delayed ring neural network extends the stability region in the parameters space, if the number of the neurons is sufficiently large. If the number of neurons is small, then a "paradoxical" region exists in the parameters space, wherein the ring neural configuration is stable, while the linear one is unstable. We study the conditions under which the paradoxical region is nonempty. We discuss how our mathematical modeling reflects neurosurgical operations with the severing of particular connections in the brain.
authors.affiliation: Department of Mathematics, South Ural State University, Chelyabinsk 454080, Russia. Electronic address: tanechkakhokhlova@gmail.com.
authors.forename: T N
authors.initials: TN
authors.lastname: Khokhlova
authors.forename: M M
authors.initials: MM
authors.lastname: Kipnis
mesh_terms: D000465:Algorithms; D001921:Brain / Q000601:surgery; D006801:Humans; D008959:Models, Neurological; D015233:Models, Statistical; D016571:Neural Networks, Computer; D009474:Neurons; D009493:Neurosurgery; D017711:Nonlinear Dynamics
keywords: Linear and ring neural configuration; Neural networks; Stability; The stability cone; Time delay