Abstract
<abstract><p>Neural networks (NNs) with values in multidimensional domains have lately attracted the attention of researchers. Thus, complex-valued neural networks (CVNNs), quaternion-valued neural networks (QVNNs), and their generalization, Clifford-valued neural networks (ClVNNs) have been proposed in the last few years, and different dynamic properties were studied for them. On the other hand, time scale calculus has been proposed in order to jointly study the properties of continuous time and discrete time systems, or any hybrid combination between the two, and was also successfully applied to the domain of NNs. Finally, in real implementations of NNs, time delays occur inevitably. Taking all these facts into account, this paper discusses ClVNNs defined on time scales with leakage, time-varying delays, and infinite distributed delays, a type of delays which have been relatively rarely present in the existing literature. A state feedback control scheme and a generalization of the Halanay inequality for time scales are used in order to obtain sufficient conditions expressed as algebraic inequalities and as linear matrix inequalities (LMIs), using two general Lyapunov-like functions, for the exponential synchronization of the proposed model. Two numerical examples are given in order to illustrate the theoretical results.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference52 articles.
1. J. K. Pearson, D. L. Bisset, Neural networks in the Clifford domain, In Proceedings of 1994 IEEE International Conference on Neural Networks (ICNN'94), IEEE, 1994. https://doi.org/10.1109/icnn.1994.374502
2. J. R. Vallejo, E. Bayro-Corrochano, Clifford Hopfield Neural Networks, In 2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence), IEEE, 2008. https://doi.org/10.1109/ijcnn.2008.4634314
3. Y. Liu, P. Xu, J. Lu, J. Liang, Global stability of Clifford-valued recurrent neural networks with time delays, Nonlinear Dyn., 84 (2015), 767–777. https://doi.org/10.1007/s11071-015-2526-y
4. Y. Li, J. Xiang, Existence and global exponential stability of anti-periodic solution for Clifford-valued inertial Cohen–Grossberg neural networks with delays, Neurocomputing, 332 (2019), 259–269. https://doi.org/10.1016/j.neucom.2018.12.064
5. B. Li, Y. Li, Existence and Global Exponential Stability of Almost Automorphic Solution for Clifford-Valued High-Order Hopfield Neural Networks with Leakage Delays, Complexity, 2019 (2019), 6751806. https://doi.org/10.1155/2019/6751806