Abstract
In this paper, in order to obtain more accurate settling time estimation and overcome the complexity of the theoretical analysis caused by using decomposition method, the problem of fixed-time (F-T) and preassigned-time (P-T) synchronization of delayed octonion-valued neural networks with impulsive effects is explored by utilizing direct octonion approach. First, a new fixed-time stability theorem for impulsive system is presented by using the comparison principle, average impulsive interval and Bernoulli differential equation theory. Second, to solve the problems of non associative and non commutative laws of octonion, some novel lemmas are introduced, which are the basis of the direct octonion approach. Third, under the improved F-T stability result, a new P-T stability theorem is derived and the settling time is preassigned according to realistic need and is irrelevant with any initial values and any parameters. Then, based on newly established theorems and developed controller strategies, some sufficient conditions are deduced to guarantee F-T and P-T synchronization of the discussed systems. Finally, a numerical simulation is provided to verify the effectiveness of the theoretical results.
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