Pattern Formation and Continuation in a Trineuron Ring with Delays  

作　　者：Shang Jiang GUO Li Hong HUANG 

机构地区：[1]College of Mathematics and Econometrics, Hu'nan University, Changsha 410082, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第5期799-818,共20页数学学报（英文版）

基　　金：This work is partially supported by the National Natural Science Foundation of P.R.China (Grant Nos.10371034 and 10271044);by the Science Foundation of Hunan University

摘　　要：In this paper, we consider a single-directional ring of three neurons with delays. First, linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. Next, we studied the local Hopf bifurcations and the spatio-temporal patterns of Hopf bifurcating periodic orbits. Basing on the normal form approach and the center manifold theory, we derive the formula for determining the properties of Hopf bifurcating periodic orbit, such as the direction of Hopf bifurcation. Finally, global existence conditions for Hopf bifurcating periodic orbits are derived by using degree theory methods.In this paper, we consider a single-directional ring of three neurons with delays. First, linear stability of the model is investigated by analyzing the associated characteristic transcendental equation. Next, we studied the local Hopf bifurcations and the spatio-temporal patterns of Hopf bifurcating periodic orbits. Basing on the normal form approach and the center manifold theory, we derive the formula for determining the properties of Hopf bifurcating periodic orbit, such as the direction of Hopf bifurcation. Finally, global existence conditions for Hopf bifurcating periodic orbits are derived by using degree theory methods.

关 键 词：ring networks periodic solution Hopf bifurcation stability 

分 类 号：TP393.12[自动化与计算机技术—计算机应用技术] TP183[自动化与计算机技术—计算机科学与技术]