Applied aspects in informatics
Mathematical models of socio-economic processes
Dynamic systems
R. I. Zemlyansky, O. I. Ryabkov On the Chaotic Dynamics of Detailed KIII Freeman Model Investigation
Scientometrics and management science
Recognition of images
R. I. Zemlyansky, O. I. Ryabkov On the Chaotic Dynamics of Detailed KIII Freeman Model Investigation


Previously in paper [1] we investigated chaotic dynamics of the simplified Walter Freeman KIII model. As mentioned in [2] this type of neural networks could be applied to solve different problems like pattern recognition and time series prediction. This makes it at least theoretically useful in the realm of computer networks security and discovery of computer attacks. In the present work we consider more complex and detailed version of this model. The main result of this article is numerical and bifurcation analysis of chaotic dynamics in detailed version of KIII network. The main focus is on chaotic attractors corresponding to basic state of the system. These attractors were originally discovered in the works of Walter Freeman and co-authors [3], [4]. Bifurcation scenario in KIII network discovered in the present work contributed to our knowledge about structure of these so-called ‘basic’ attractors.


chaotic dynamics, nonlinear dynamics, neural networks, KIII model, attractor, differential equations, delay differential equations.

PP. 44-53.


1. Zemlyansky R.I., Ryabkov O.I., Ob issledovanii scenariya perehoda k haosu v KIII modeli Waltera Freemena [On the  investigation of route to chaos in Walter Freeman KIII model] // Trudi ISA RAN [Proceedings of ISA RAS]. 2016. Vol. 66. № 3.  P. 38 – 44. (In Russian.)
2. Ryabkov O.I., O primenenii dinamicheskih system v zadachah obrabotki informazii [On the application of dynamical systems  to the information processing] // Trudi ISA RAN [Proceedings of ISA RAS]. 2015. Vol. 65. № 2. P. 8–17. (In Russian.)
3. Freeman W.J., Simulation of Chaotic EEG Patterns with a Dynamic Model of the Olfactory System //Biological Cybernetics.  No. 56. P.139 – 150. 1987.
4. Yong Yao, Freeman W.J., Model of Biological Pattern Recognition with Spatially Chaotic Dynamics // Neural Networks. 1990.  Vol. 3. PP. 153 – 170.
5. Kozma R., Beliaev I., Time Series Prediction Using Chaotic Neural Networks: Case Study of IJCNN CATS Benchmark Test //  IEEE International Joint Conference on Neural Networks Proceedings. 2004.
6. Guang Li, Zhang Jin, and Freeman W.J., Mandarin Digital Speech Recognition Based on a Chaotic Neural Network and Fuzzy  C-means Clustering // IEEE International Fuzzy Systems Conference Proceedings. 2007.
7. Xu Li, Guang Li, Le Wang, Freeman W.J., A Study on a Bionic Pattern Classifier Based onOlfactory Neural System //  International Journal of Bifurcation and Chaos. 2006. Vol. 16. No. 8. PP. 2425–2434.
8. Guoguang Hea, Luonan Chena, Kazuyuki Aihara, Associative memory with a controlled chaotic neural network  //Neurocomputing. 2008. V. 71. P. 2794–2805.
9. FitzHugh R., Mathematical models of threshold phenomena in the nerve membrane // Bull. Math. Biophysics. 1955. V. 17 P.  257—278.
10. Blue Brain Project Page. URL: http://bluebrain.
11. Beliaev I., Kozma R., Studies on the Memory Capacity and Robustness of Chaotic Dynamic Neural Networks //IEEE  International Joint Conference on Neural Network Proceedings. 2006.
12. Magnitskii N.A., Sidorov S.V., Novie methodi haoticheskoy dinamiki [New methods of chaotic dynamics]. - Moscow:  Editorial URSS, 2004. (In Russian.)
13. Magnitskii N.A., Teoriya dinamicheskogo haosa [Theory of dynamical chaos]. - Moscow: Editorial URSS, 2011. (In Russian.)
14. Hairer E., Nørsett S.P., Wanner G., Solving Ordinary Differential Equations I: Nonstiff Problems. – Springer Science &  Business Media. January 1993.
15. C.A.H. Paul, C.T.H. Baker, Explicit Runge-Kutta Methods for the Numerical Solution of Singular Delay Differential Equations  // Numerical Analysis Report. April 1992. No.212.
16. Anishchenko V., Nikolaev S., Winding number locking on a two-dimensional torus: Synchronization of quasiperiodic  motions // Physical Review E. 2006. V.73. 056202.


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