Dynamics of Anti-Periodic Solutions for Inertial Quaternion-Valued Hopfield Neural Networks with Time-Varying Delays
Received:July 29, 2020  Revised:April 06, 2021
Key Word: anti-periodic solution   asymptotic stability   continuation theorem   Quaternion-valued inertial neural networks  
Fund ProjectL:Supported by the Basic Research Expenses for Provincial Colleges and Universities (Grant No.JYT2020030).
Author NameAffiliation
Ailing LI College of Science, Hebei North University, Hebei 075000, P. R. China 
Mengting LV School of Mathematics, Hunan University, Hunan 410082, P. R. China 
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      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.
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