Abstract
Abstract Octonion-valued neural networks (OVNNs) are a type of neural networks for which the states and weights are octonions. The octonion algebra is the only normed division algebra that can be defined over the reals, besides the complex and quaternion algebras. Being nonassociative, it clearly does not belong to the Clifford algebras category, which are all associative. In this paper, sufficient conditions for the global exponential stability of neutral-type OVNNs with time-varying delays are formulated, by considering two types of Lipschitz conditions that must be satisfied by the octonion-valued activation functions. To avoid the nonassociativity of the octonions and the noncommutativity of the quaternions, the OVNNs model is decomposed into 4 complex-valued systems, using the Cayley–Dickson construction. By using Lyapunov–Krasovskii functionals with double, triple, and quadruple integral terms, the free weighting matrix method, and simple, double, and triple Jensen inequalities, the stability criteria are formulated in terms of complex-valued linear matrix inequalities. Two numerical examples are provided in order to demonstrate the effectiveness and feasibility of the theoretical results.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
