Asymptotic stability for quaternion-valued fuzzy BAM neural networks via integral inequality approach

The existence-uniqueness (EU) and globally asymptotic stability (GAS) of equilibrium solutions (ESS) for a class of quaternion-valued fuzzy BAM neural networks (QVFBAMNNS) with delays are concerned. Firstly, by using Homeomorphism theorem (HT) and by using the properties of unary high degree inequality, a sufficient condition ensuring the EU of ESS of the concerned QVFBAMNNS is achieved. Then, without utilizing V′(t)≤0, by applying integral inequality approach (IIA), a condition assuring the GAS of ESS for above networks is achieved. Utilizing the properties of high degree inequality studies the EU of ESS and utilizing IIA studies the GAS for neural networks (NNS) are new research approaches.