Generation of cyclic/toroidal chaos by Hopfield neural networks

Date

2014-12-05

Author

Akhmet, Marat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

230
views

0
downloads

We discuss the appearance of cyclic and toroidal chaos in Hopfield neural networks. The theoretical results may strongly relate to investigations of brain activities performed by neurobiologists. As new phenomena, extension of chaos by entrainment of several limit cycles as well as the attraction of cyclic chaos by an equilibrium are discussed. Appropriate simulations that support the theoretical results are depicted. Stabilization of tori in a chaotic attractor is realized not only for neural networks, but also for differential equations theory, and this phenomenon has never been reported before in the literature. It is demonstrated that the proposed chaos generation technique cannot be considered as generalized synchronization.

Subject Keywords

Cognitive Neuroscience, Artificial Intelligence, Computer Science Applications

URI

https://hdl.handle.net/11511/38886

Journal

NEUROCOMPUTING

DOI

https://doi.org/10.1016/j.neucom.2014.05.038

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Attraction of Li-Yorke chaos by retarded SICNNs Akhmet, Marat (Elsevier BV, 2015-01-05) 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 b...
Improving forecasting accuracy of time series data using a new ARIMA-ANN hybrid method and empirical mode decomposition Buyuksahin, Umit Cavus; Ertekin Bolelli, Şeyda (Elsevier BV, 2019-10-07) Many applications in different domains produce large amount of time series data. Making accurate forecasting is critical for many decision makers. Various time series forecasting methods exist that use linear and nonlinear models separately or combination of both. Studies show that combining of linear and nonlinear models can be effective to improve forecasting performance. However, some assumptions that those existing methods make, might restrict their performance in certain situations. We provide a new Au...
Robust semi-supervised clustering with polyhedral and circular uncertainty DİNLER, DERYA; Tural, Mustafa Kemal (Elsevier BV, 2017-11-22) 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...
Nuclear Fission-Nuclear Fusion algorithm for global optimization: a modified Big Bang-Big Crunch algorithm YALÇIN, YAĞIZER; Pekcan, Onur (Springer Science and Business Media LLC, 2020-04-01) This study introduces a derivative of the well-known optimization algorithm, Big Bang-Big Crunch (BB-BC), named Nuclear Fission-Nuclear Fusion-based BB-BC, simply referred to as N2F. Broadly preferred in the engineering optimization community, BB-BC provides accurate solutions with reasonably fast convergence rates for many engineering problems. Regardless, the algorithm often suffers from stagnation issues. More specifically, for some problems, BB-BC either converges prematurely or exploits the promising r...
Fuzzy model tuning using simulated annealing Yanar, Tahsin Alp; Akyürek, Sevda Zuhal (Elsevier BV, 2011-07-01) This paper presents the use of simulated annealing metaheuristic for tuning Mamdani type fuzzy models. Structure of the Mamdani fuzzy model is learned from input-output data pairs using Wang and Mendel's method and fuzzy c-means clustering algorithm. Then, parameters of the fuzzy system are tuned through simulated annealing. In this paper, we perform experiments to examine effects of (a) initial solution generated by Wang and Mendel's method and fuzzy c-means clustering method, (b) membership function updat...

Citation Formats

M. Akhmet, “Generation of cyclic/toroidal chaos by Hopfield neural networks,” NEUROCOMPUTING, pp. 230–239, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38886.