Asymptotic Stability of a Class of Neutral Delay Neuron System in a Critical Case. Academic Article

abstract

• In this brief, the asymptotic stability properties of a neutral delay neuron system are studied mainly in a critical case when the exponential stability is not possible. If a critical value of the coefficient in the neutral delay neuron system is considered, then the difficulty for our investigation is caused by the fact that the spectrum of the linear operator is asymptotically approximated to the imaginary axis. It is obvious that, in such a case, the equation is not exponentially stable, and one needs more subtle methods in order to characterize this type of asymptotic stability. Hence, first, the local asymptotic stability for the neutral delay neuron system is studied, and the main tools involved are the asymptotic expansions of characteristic roots, Laplace transforms, and function series, and a complete analysis of the stability diagram is also presented. Then, based on the energy method, the globally asymptotic stability results for the neutral delay neuron system are derived.

authors

• Huang, Tingwen

published proceedings

• IEEE Trans Neural Netw Learn Syst

author list (cited authors)

• Liao, X., & Huang, T.

citation count

• 7

complete list of authors

• Liao, Xiaofeng||Huang, Tingwen

publication date

• December 2015

publisher

• Institute of Electrical and Electronics Engineers (IEEE)  Publisher

published in

• IEEE Transactions on Neural Networks and Learning Systems  Journal

keywords

• Algorithms
• Computer Simulation
• Humans
• Models, Neurological
• Neural Networks, Computer
• Neurons
• Nonlinear Dynamics
• Time Factors

Digital Object Identifier (DOI)

• 10.1109/TNNLS.2015.2469148

start page

• 3320

end page

• 3325

volume

• 26

issue

• 12

URL

• http://dx.doi.org/10.1109/tnnls.2015.2469148