Biological Cybernetics

, Volume 64, Issue 1, pp 15–23 | Cite as

Creative dynamics approach to neural intelligence



The thrust of this paper is to introduce and discuss a substantially new type of dynamical system for modelling biological behavior. The approach was motivated by an attempt to remove one of the most fundamental limitations of artificial neural networks — their rigid behavior compared with even simplest biological systems. This approach exploits a novel paradigm in nonlinear dynamics based upon the concept of terminal attractors and repellers. It was demonstrated that non-Lipschitzian dynamics based upon the failure of Lipschitz condition exhibits a new qualitative effect — a multi-choice response to periodic external excitations. Based upon this property, a substantially new class of dynamical systems — the unpredictable systems — was introduced and analyzed. These systems are represented in the form of coupled activation and learning dynamical equations whose ability to be spontaneously activated is based upon two pathological characteristics. Firstly, such systems have zero Jacobian. As a result of that, they have an infinite number of equilibrium points which occupy curves, surfaces or hypersurfaces. Secondly, at all these equilibrium points, the Lipschitz conditions fails, so the equilibrium points become terminal attractors or repellers depending upon the sign of the periodic excitation. Both of these pathological characteristics result in multi-choice response of unpredictable dynamical systems. It has been shown that the unpredictable systems can be controlled by sign strings which uniquely define the system behaviors by specifying the direction of the motions in the critical points. By changing the combinations of signs in the code strings the system can reproduce any prescribed behavior to a prescribed accuracy. That is why the unpredictable systems driven by sign strings are extremely flexible and are highly adaptable to environmental changes. It was also shown that such systems can serve as a powerful tool for temporal pattern memories and complex pattern recognition. It has been demonstrated that new architecture of neural networks based upon non-Lipschitzian dynamics can be utilized for modelling more complex patterns of behavior which can be associated with phenomenological models of creativity and neural intelligence.


Equilibrium Point Pathological Characteristic Complex Pattern Lipschitz Condition External Excitation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. Annionos PA, Beek B, Csermely TJ, Harth E, Pertile G (1970) Dynamics of neural structures. J Theor Biol 26:121–148PubMedGoogle Scholar
  2. Basar E (1980) EEG-brain dynamics. Elsevier, AmsterdamGoogle Scholar
  3. Daan S, Berde C (1978) Two coupled oscillators: simulations of the circadian pacemaker in mammalian activity rhythms. J Theor Biol 70:297–313CrossRefPubMedGoogle Scholar
  4. Harth E, Csermely TJ, Beek B, Lindsay RD (1970) Brain functions and neural dynamics. J Theor Biol 26:93–120PubMedGoogle Scholar
  5. Nicolis JS (1985) Chaotic dynamics of information processing with relevance to cognitive brain functions. Kybernetes 14:167–172Google Scholar
  6. Schöner G, Kelso JAS (1988) A synergetic theory of environmentally-specified and learned patterns of movement coordination. Biol Cybern 58:81–89CrossRefPubMedGoogle Scholar
  7. Zak M (1987) Deterministic representation of chaos with application to turbulence. Math Model 9:599–612CrossRefGoogle Scholar
  8. Zak M (1988) Terminal attractors for associative memory in neural networks. Phys Lett A 133:18–22CrossRefGoogle Scholar
  9. Zak M (1989a) Non-Lipschitzian dynamics for neural net modelling. Appl Math Lett 2:69–74CrossRefGoogle Scholar
  10. Zak M (1989b) Terminal attractors networks. Neural Network 2:(3)Google Scholar
  11. Zak M (1990a) Spontaneously activated systems in neurodynamics. Complex Syst 3Google Scholar
  12. Zak M (1990b) Weakly connected neural nets. Appl Math Lett 3:(3)Google Scholar
  13. Zak M (1990c) Creative dynamics approach to neural intelligence. Proceedings of the Fourth Annual Parallel Processing Symposium, April 4–6, 1990, pp 262–288Google Scholar
  14. Zak M, Barhen J (1989) Neural networks with creative dynamics, 7th Int. Conference on Math and Computer Modelling, Aug. 2–5, 1989, Chicago, IllGoogle Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • M. Zak
    • 1
  1. 1.Center for Microelectronics Technology, Jet Propulsion LaboratoryCalifornia Institute of TechnologyPasadenaUSA

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