Impulsive Destabilization Effect on Novel Existence of Solution and Global μ -Stability for MNNs in Quaternion Field

Qingchao Meng and Huamin Wang ()
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Qingchao Meng: College of Artificial Intelligence, Southwest University, Chongqing 400715, China
Huamin Wang: College of Artificial Intelligence, Southwest University, Chongqing 400715, China

Mathematics, 2023, vol. 11, issue 8, 1-12

Abstract: In this paper, a novel memristor-based non-delay Hopfield neural network with impulsive effects is designed in a quaternion field. Some special inequalities, differential inclusion, Hamilton rules and impulsive system theories are utilized in this manuscript to investigate potential solutions and obtain some sufficient criteria. In addition, through choosing proper μ ( t ) and impulsive points, the global μ -stability of the solution is discussed and some sufficient criteria are presented by special technologies. Then, from the obtained sufficient criteria of global μ -stability, other stability criteria including exponential stability and power stability can be easily derived. Finally, one numerical example is given to illustrate the feasibility and validity of the derived conclusions.

Keywords: ? -stability; quaternion field; memristor-based Hopfield neural networks; impulsive destabilization; exponential stability (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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