Dynamics of Anti-Periodic Solutions for Inertial Quaternion-Valued Hopfield Neural Networks with Time-Varying Delays  

作　　者：Ailing LI Mengting LV 

机构地区：[1]College of Science,Hebei North University,Hebei 075000,P.R.China [2]School of Mathematics,Hunan University,Hunan 410082,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2021年第5期461-472,共12页数学研究及应用（英文版）

基　　金：Supported by the Basic Research Expenses for Provincial Colleges and Universities(Grant No.JYT2020030)。

摘　　要：Periodicity, anti-periodicity and almost periodicity are significant dynamic behaviors of time-varying neural networks. This paper researches the dynamics of anti-periodic solutions for a kind of inertial Quaternion-valued Hopfield neural networks with varying-time delays.Without resolving the explored neural networks into real-valued systems, in the light of a continuation theorem of coincidence degree theory and inequality skills, by constructing different Lyapunov functions from those constructed in the existing research of the stability of equilibrium point, periodic solutions and anti-periodic solutions for neural networks, a newfangled sufficient condition insuring the existence of periodic solutions for above neural networks is gained. By constructing the same Lyapunov functions as those constructed in the proof of the existence of anti-periodic solutions, the newfangled asymptotic stability of anti-periodic solutions for above networks is acquired.

关 键 词：anti-periodic solution asymptotic stability continuation theorem Quaternion-valued inertial neural networks 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]