A note on convergence under dynamical thresholds with delays

Abstract

We complement the study of the asymptotic behaviour of the dynamical threshold neuron model with delay, introduced by Gopalsamy and Leung, by providing a description of the dynamics of the system in the remaining parameters range. We characterize the regions of "harmless" delays and those in which delay-induced oscillations appear.

Codimension-two bursting analysis in the delayed neural system with external stimulations

“…On the base of the previous researches, in 1998, Pakdaman et al [8] provided a class of delayed neural network with the graded-response continuous-time neurons. Also, they especially researched the duration of the transient oscillation [8], the asymptotic convergence [9], and attraction basins of the equilibrium [10,11] in a one-or two-neural delayed system through the analytical methods, which is the foundation of our further studies. Recently, for this delayed neural system, we have researched the bifurcation dynamics and obtained the different type of bursting behaviors.…”

System Identification with Quantized Observations

“…Additionally, quantized sensors are commonly employed in practical systems [10,42,49,73,90,98,99]. Usually they are more cost-effective than regular sensors.…”

“…This learning problem can be formulated as a special case of binary sensor identification without unmodeled dynamics. Traditional neural models, such as the McCulloch-Pitts and Nagumo-Sato models, contain a neural firing threshold that naturally introduces a binary function [13,38,42,73]. Fundamental stochastic neural learning theory studies the stochastic updating algorithms for neural parameters [94,95,96].…”

“…Its theoretical foundation and main properties have been studied in a different context beyond sampled date systems; see [1,34,80]. Quantized information processing occurs in many different applications beyond system identification [13,38,39,73,96]. Identification input design is an integral part of an identification experiment.…”

“…For some related but different identification algorithms such as binary reinforcement and some applications, the reader is referred to [2,13,18,27,29,33,73,119]. The main tools for stochastic analysis and identification methodologies can be found in [8,17,30,31,55,62,76,83].…”