Bidirectional Associative Memory Neural Networks Involving Zones of No Activation/Dead Zones

Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 834)

Abstract

This article purports to present a systematically developed survey on the influence of zones of no activation/dead zones in bidirectional associative memory (BAM) neural networks. The modeling effort based on the concept of dead zones is capable of explaining very intricate phenomena concerned with the functioning of the human brain. Activation dynamic models presented in this article provide a platform for the development of artificial neural network models. Several questions of importance that arise in the modeling of these systems have been discussed in this article. More precisely, the influence of a dead zone on the global stability, which is associated with the recall of memories, is investigated and various easily verifiable sets of sufficient conditions are provided. Directions for further research related to the incorporation of various possible kinds of dead zones that occur naturally in biological or artificial systems are discussed.

References

  1. 1.
    Anderson, J.: A memory storage model utilizing spatial correlation functions. Kybernetik 5, 113–119 (1968)CrossRefGoogle Scholar
  2. 2.
    Anderson, J.: Two models for memory organization using interacting traces. Math. Biosci. 8, 137–160 (1970)CrossRefGoogle Scholar
  3. 3.
    Anderson, J.: A simple neural network generating an interactive memory. Math. Biosci. 14, 197–220 (1972)CrossRefGoogle Scholar
  4. 4.
    Anderson, J.: A theory for the recognition of items from short memorized lists. Psych. Rev. 80, 417–438 (1973)CrossRefGoogle Scholar
  5. 5.
    Chen, F.-C., Liu, C.-C.: Adaptively controlling nonlinear continuous-time systems using multilayer neural networks. IEEE Trans. Automat. Control 39, 1306–1310 (1994)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Chen, F.-C., Khalil, H.K.: Adaptive control of nonlinear systems using neural networks - a dead zone approach. In: Proceedings of the 1991 American Control Conference, pp. 667–672 (1991)Google Scholar
  7. 7.
    Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Nat. Acad. Sci. 79, 2554–2558 (1982)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hopfield, J.J.: Neurons with graded response have collective computational properties like those of two state neurons. Proc. Nat. Acad. Sci. 81, 3088–3092 (1984)CrossRefGoogle Scholar
  9. 9.
    Hopfield, J.J., Feinstein, D., Palmer, R.: Unlearning has a stabilizing effect in collective memories. Nature 304, 158–159 (1983)CrossRefGoogle Scholar
  10. 10.
    Kohonen, T.: Self-Organization and Associative Memory. Springer, New York (1988).  https://doi.org/10.1007/978-3-642-88163-3CrossRefMATHGoogle Scholar
  11. 11.
    Kohonen, T.: Correlative associative memory. IEEE Trans. Comput. C-21, 353–359 (1972)Google Scholar
  12. 12.
    Kohonen, T.: Associative Memory - A System Theoretical Approach. Springer, New York (1977).  https://doi.org/10.1007/978-3-642-96384-1CrossRefMATHGoogle Scholar
  13. 13.
    Kosko, B.: Adaptive bidirectional associative memories. Appl. Opt. 26, 4947–4960 (1987)CrossRefGoogle Scholar
  14. 14.
    Kosko, B.: Bidirectional associative memories. IEEE Trans. Syst. Man Cybern. SMC 18, 49–60 (1988)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Kosko, B.: Feedback stability and unsupervised learning. In: Proceedings of the IEEE International Conference on Neural Networks, vol. I, pp. 141–152. IEEE, San Diego (1988)Google Scholar
  16. 16.
    Kosko, B.: Neural Networks and Fuzzy Systems - A Dynamical Systems Approach to Machine Intelligence. Prentice-Hall of India, New Delhi (1994)MATHGoogle Scholar
  17. 17.
    Lala, P.K.: Fault Tolerant and Fault Testable Design. Prentice Hall International, Upper Saddle River (1985)Google Scholar
  18. 18.
    Lindsay, P., Norman, D.: Human Information Processing: An Introduction to Psychology. Academic Press, Orlando (1977)Google Scholar
  19. 19.
    Selmic, R.R., Lewis, F.L.: Dead zone compensation in motion control systems using neural networks. IEEE TAC 45(4), 602–613 (2000)MATHGoogle Scholar
  20. 20.
    Simpson, P.K.: Artificial Neural Systems - Foundations, Paradigms, Applications and Implementations. Pergamon Press, New York (1989)Google Scholar
  21. 21.
    Shyu, K.K., Liu, H.J., Hsu, K.C.: Design of large scale time delayed systems with dead zone input via variable structure control. Automatica 41(7), 1239–1246 (2005)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Sree Hari Rao, V., Phaneendra, Bh.R.M., Prameela, V.: Global dynamics of bidirectional associative memory networks with transmission delays. Diff. Equ. Dyn. Syst. 4, 453–471 (1996)Google Scholar
  23. 23.
    Sree Hari Rao, V., Phaneendra, Bh.R.M.: Global dynamics of bidirectional associative memory neural networks with transmission delays and dead zones. Neural Netw. 12, 455–465 (1999)Google Scholar
  24. 24.
    Sree Hari Rao, V., Raja Sekhara Rao, P.: Stability of dead zone bidirectional associative memory neural networks involving time delays. Int. J. Neural Syst. 12(1), 15–29 (2002)CrossRefGoogle Scholar
  25. 25.
    Sree Hari Rao, V., Raja Sekhara Rao, P.: Time varying stimulations in simple neural networks and convergence to desired outputs. Diff. Equ. Dyn. Syst. 26, 81–104 (2016).  https://doi.org/10.1007/s12591-016-0312-zMathSciNetCrossRefMATHGoogle Scholar
  26. 26.
    Wang, X.S., Hong, H., Su, C.Y.: Robust adaptive control of a class of nonlinear systems with an unknown dead zones. Automatica 40(3), 407–413 (2004)MathSciNetCrossRefGoogle Scholar
  27. 27.
    Zhang, T., Sam Ge, S.: Adaptive neural network tracking control of MIMO nonlinear systems with unknown dead zones and control directions. IEEE Trans. Neural Netw. 20, 483–497 (2009)CrossRefGoogle Scholar
  28. 28.
    Zhou, J., Er, M.J., Veluvollu, K.C.: Adaptive output control of nonlinear time delayed systems with uncertain dead zone input. In: Proceedings of American Control Conference, Minneapolis, MN, 14–16 June 2006, pp. 5312–5316 (2006)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMissouri University of Science & TechnologyRollaUSA
  2. 2.Foundation for Scientific Research and Technological Innovation (FSRTI)HyderabadIndia
  3. 3.Government PolytechnicKalidindiIndia

Personalised recommendations