Attraction of Li-Yorke chaos by retarded SICNNs

In the present study, dynamics of retarded shunting inhibitory cellular neural networks (SICNNs) is investigated with Li-Yorke chaotic external inputs and outputs. Within the scope of our results, we prove the presence of generalized synchronization in coupled retarded SICNNs, and confirm it by means of the auxiliary system approach. We have obtained more than just synchronization, as it is proved that the Li-yorke chaos is extended with its ingredients, proximality and frequent separation, which have not been considered in the theory of synchronization at all. Our procedure is used to synchronize chains of unidirectionally coupled neural networks. The results may explain the high performance of brain functioning and can be extended by specific stability analysis methods. Illustrations supporting the results are depicted. For the first time in the literature, proximality and frequent separation features are demonstrated numerically for continuous-time dynamics.


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We consider a semi-supervised clustering problem where the locations of the data objects are subject to uncertainty. Each uncertainty set is assumed to be either a closed convex bounded polyhedron or a closed disk. The final clustering is expected to be in accordance with a given number of instance level constraints. The objective function considered minimizes the total of the sum of the violation costs of the unsatisfied instance level constraints and a weighted sum of squared maximum Euclidean distances b...
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The Hopfield network is a form of recurrent artificial neural network. To satisfy demands of artificial neural networks and brain activity, the networks are needed to be modified in different ways. Accordingly, it is the first time that, in our paper, a Hopfield neural network with piecewise constant argument of generalized type and constant delay is considered. To insert both types of the arguments, a multi-compartmental activation function is utilized. For the analysis of the problem, we have applied the ...
ANFIS_unfolded_in_time for multivariate time series forecasting
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This paper proposes a temporal neuro-fuzzy system named ANFIS_unfolded_in_time which is designed to provide an environment that keeps temporal relationships between the variables and to forecast the future behavior of data by using fuzzy rules. It is a modification of ANFIS neuro-fuzzy model. The rule base of ANFIS_unfolded_in_time contains temporal TSK(Takagi-Sugeno-Kang) fuzzy rules. In the training phase, back-propagation learning algorithm is used. The system takes the multivariate data and the number o...
Citation Formats
M. Akhmet, “Attraction of Li-Yorke chaos by retarded SICNNs,” NEUROCOMPUTING, pp. 330–342, 2015, Accessed: 00, 2020. [Online]. Available: