Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays | Zendy

Yaping Ren | Zendy; Yongkun Li | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Bifurcation Analysis for a Two-Dimensional Discrete-Time Hopfield Neural Network with Delays

Author(s) -

Yaping Ren,

Yongkun Li

Publication year - 2007

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2007/84260

Subject(s) - center manifold , mathematics , discrete time and continuous time , hopfield network , bifurcation , saddle node bifurcation , biological applications of bifurcation theory , bifurcation diagram , transcritical bifurcation , artificial neural network , stability (learning theory) , period doubling bifurcation , hopf bifurcation , mathematical analysis , computer science , nonlinear system , artificial intelligence , statistics , physics , quantum mechanics , machine learning

A bifurcation analysis is undertaken for a discrete-time Hopfield neural network with four delays. Conditions ensuring the asymptotic stability of the null solution are obtained with respect to two parameters of the system. Using techniques developed by Kuznetsov to a discrete-time system, we study the Neimark-Sacker bifurcation (also called Hopf bifurcation for maps) of the system. The direction and the stability of the Neimark-Sacker bifurcation are investigated by applying the normal form theory and the center manifold theorem

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research