Abstract
We proposed and realized one new type models of neural networks, which takes into account property of anticipation. As the base model, the Hopfield type models with anticipation have been explored. The basic new qualities, discovered at research there is that possible multi-valued solutions of given neural networks. Different types of behaviour of such systems have been explored depending on parameters of networks. Some problems of self-organized behaviour are proposed. The problems of complex solutions and stored information have been considered, including the measures of complexity in deterministic and non-deterministic cases. Presumable applications of such models for living and social systems are discussed.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Haykin, S.: Neural Networks. A Comprehensive Foundation, 2nd edn. Prentice Hall, New Jersey (1999)
Hertz, J., Krogh, A., Palmer, R.G.: Introduction to the Theory of Neural Computation. Addison-Wesley, Reading (1991)
Sipser, M.: Introduction to the Theory of Computation, 2nd edn. Thomson Course Technology, USA (2006)
Aubin, J.-P.: Neural Networks and Qualitative Physics. Cambridge University Press, Cambridge (1996)
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. U.S.A 79(8), 2554–2558 (1982)
Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Nat. Acad. Sci. U.S.A 79(8), 2554–2558 (1984)
Sutton, J.P., Beis, J.S., Trainor, L.E.H.: Hierarchical model of memory and memory loss. J. Phys. A: Math. Gen. 21, 4443–4454 (1988)
Guyon, I., Personnaz, L., Nadal, J.P., Dreyfus, G.: Storage and retrieval of complex sequences in neural networks. Phys. Rev. A 38(12), 6365–6372 (1988)
Chua, L.O., Yang, L.: Cellular neural networks: Theory. IEEE Trans. Circuits Syst. I 35, 1257−1272 (1988)
Jankowski, S., Lozowski, A., Zarada, J.M.: Complex-valued multistate neural associative memory. IEEE Trans. Neural Netw. 6(6), 1491–1496 (1996)
Forti, M., Grazzini, M., Nistri, P., Pancioni, L.: Generalized Lyapunov approach for convergence of neural networks with discontinuous or non–lipshitz activations. Physica D 214, 88–99 (2006)
Forti, M., Nistri, P.: Global convergence of neural networks with discontinuous neuron activation. IEEE Trans. Circuits Syst.—I Fundam. Theory Appl. 50 (11), 1421—1435 (2003)
Makarenko, A.: Anticipating in modeling of large social systems—neuronets with internal structure and multivaluedness. Int. J Comput. Anticipatory Syst. 13, 77–92 (2002)
Makarenko, A.: Anticipatory agents, scenarios approach in decision-making and some quantum–mechanical analogies. Int. J Comput. Anticipatory Syst. 15, 217–225 (2004)
Makarenko, A., Stashenko, A.: Some two-steps discrete-time anticipatory models with ‘boiling’ multivaluedness. In: Dubois, D.M. (ed.) American Institute of Physics, AIP Conference Proceedings, vol. 839, pp. 265−272 (2006)
Rosen, R.: Anticipatory Systems. Pergamon Press, Oxford (1985)
Dubois, D.: Introduction to computing anticipatory systems. Int. J. Comput. Anticipatory Syst. 2, 3–14 (1998)
Dubois, D.: Incursive and hyperincursive systems, fractal machine and anticipatory logic. In: Computing Anticipatory Systems: CASYS 2000—The Fourth International Conference. American Institute of Physics, AIP Conference Proceedings, vol. 573, pp. 437−451 (2001)
Scharkovski, A., Maystrenko, Yu., Romanenko, E.: Discrete Equations and Their Applications. Kluwer Academic, Dordrecht (1993)
Makarenko, A.: Cellular Automata with anticipation: some new research problems. Int. J. Comput. Anticipatory Syst. (Belgium) 20, 230–242 (2008)
Makarenko, A.: On presumable role of anticipatory effects in neurophysiology and consciousness (short abstract in Russian). In: Proceedings of the XVI International Conference On Neurocybernetics (ICNC-12), 3 pp. Rostov-on-Don, Russia 24−28 Sept 2012
Acknowledgements
The author is gratitude for A. Yatsuk and V. Biluga for the help in numerical calculations.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Makarenko, O.S. (2016). Neural Networks with Strong Anticipation and Some Related Problems of Complexity Theory. In: Dimirovski, G. (eds) Complex Systems. Studies in Systems, Decision and Control, vol 55. Springer, Cham. https://doi.org/10.1007/978-3-319-28860-4_12
Download citation
DOI: https://doi.org/10.1007/978-3-319-28860-4_12
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-28858-1
Online ISBN: 978-3-319-28860-4
eBook Packages: EngineeringEngineering (R0)