Skip to main content

Timescale and Stability in Adaptive Behaviour

  • Conference paper
Advances in Artificial Life (ECAL 2005)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 3630))

Included in the following conference series:

  • 1996 Accesses

Abstract

Recently, in both the neuroscience and adaptive behaviour communities, there has been growing interest in the interplay of multiple timescales within neural systems. In particular, the phenomenon of neuromodulation has received a great deal of interest within neuroscience and a growing amount of attention within adaptive behaviour research. This interest has been driven by hypotheses and evidence that have linked neuromodulatory chemicals to a wide range of important adaptive processes such as regulation, reconfiguration, and plasticity. Here, we first demonstrate that manipulating timescales can qualitatively alter the dynamics of a simple system of coupled model neurons. We go on to explore this effect in larger systems within the framework employed by Gardner, Ashby and May in their seminal studies of stability in complex networks. On the basis of linear stability analysis, we conclude that, despite evidence that timescale is important for stability, the presence of multiple timescales within a single system has, in general, no appreciable effect on the May-Wigner stability/connectance relationship. Finally we address some of the shortcomings of linear stability analysis and conclude that more sophisticated analytical approaches are required in order to explore the impact of multiple timescales on the temporally extended dynamics of adaptive systems.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Kauffman, S.: The Origins of Order. Oxford University Press, Oxford (1993)

    Google Scholar 

  2. Gershenson, C.: Classification of random Boolean networks. In: Standish, R.K., Bedau, M.A., Abbass, H.A. (eds.) Artificial Life VIII: Proceedings of the Eight International Conference on Artificial Life, pp. 1–8. MIT Press, Cambridge (2002)

    Google Scholar 

  3. Beer, R.D.: On the dynamics of small continuous-time recurrent neural networks. Adaptive Behavior 3, 471–511 (1995)

    Article  Google Scholar 

  4. Di Paolo, E.A.: Searching for rhythms in asynchronous Boolean networks. In: Bedau, M.A., McCaskill, J.S., Packard, N.H., Rasmussen, S. (eds.) Seventh Inter- national Conference on Artificial Life. MIT Press, Cambridge (2000)

    Google Scholar 

  5. Poggio, T.A., Glaser, D.A. (eds.): Exploring Brain Functions: Models in Neuro- science. John Wiley and Sons, New York (1993)

    Google Scholar 

  6. Katz, P.S. (ed.): Beyond Neurotransmission: Neuromodulation and its Importance for Information Processing. Oxford University Press, Oxford (1999)

    Google Scholar 

  7. Turrigiano, G.G.: Homeostatic plasticity in neuronal networks: The more things change, the more they stay the same. Trends in Neuroscience 22, 221–227 (1999)

    Article  Google Scholar 

  8. Doya, K.: Metalearning and neuromodulation. Neural Networks 15, 495–506 (2002)

    Article  Google Scholar 

  9. Williams, H.: Homeostatic plasticity in recurrent neural networks. In: Schaal, S., Ijspeert, A., Billard, A., Vijayakumar, S., Hallam, J., Meyer, J.A. (eds.) Eighth International Conference on the Simulation of Adaptive Behavior, pp. 344–353. MIT Press, Cambridge (2004)

    Google Scholar 

  10. Husbands, P., Philippides, A., Smith, T.M.C., O’Shea, M.: The shifting network: Volume signalling in real and robot nervous systems. In: Kelemen, J., Sosík, P. (eds.) ECAL 2001. LNCS (LNAI), vol. 2159, pp. 23–36. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  11. Philippides, A.O., Husbands, P., Smith, T.M.C., O’Shea, M.: Fast and loose: Biologically inspired couplings. In: Standish, R.K., Bedau, M.A., Abbass, H.A. (eds.) Eighth International Conference on Artificial Life, pp. 292–301. MIT Press, Cambridge (2002)

    Google Scholar 

  12. Smith, T.M.C., Husbands, P., Philippides, A.O., O’Shea, M.: Neuronal plasticity and temporal adaptivity: GasNet robot control networks. Adaptive Behavior 10, 161–184 (2002)

    Article  Google Scholar 

  13. Smith, T.M.C., Husbands, P., O’Shea, M.: Not measuring evolvability: Initial exploration of an evolutionary robotics search space. In: Congress on Evolutionary Computation, pp. 9–16. IEEE Press, Los Alamitos (2001)

    Google Scholar 

  14. Buckley, C., Bullock, S., Cohen, N.: Toward a dynamical systems analysis of neuro- modulation. In: Schaal, S., Ijspeert, A.J., Vijayakumar, A.B.S., Hallam, J., Meyer, J.A. (eds.) Eighth International Conference on Simulation of Adaptive Behavior, pp. 334–343. MIT Press, Cambridge (2004)

    Google Scholar 

  15. Hooper, S.L.: Neural circuits: Functional reconfiguration. In: Nature Encyclopedia of Life Science. Nature Publishing Group, London (2001)

    Google Scholar 

  16. Harvey, I., Thompson, A.: Through the labyrinth evolution finds a way: A silicon ridge. In: Higuchi, T., Iwata, M., Weixin, L. (eds.) ICES 1996. LNCS, vol. 1259, pp. 406–422. Springer, Heidelberg (1997)

    Google Scholar 

  17. Strogatz, S.H.: Nonlinear Dynamics & Chaos. Addison-Wesley, Reading (1994)

    Google Scholar 

  18. Gardner, M.R., Ashby, W.R.: Connectance of large dynamic (cybernetic) systems: Critical values for stability. Nature 228, 784–784 (1970)

    Article  Google Scholar 

  19. McCann, K.S.: The diversity-stability debate. Nature 405, 228–233 (2000)

    Article  Google Scholar 

  20. May, R.M.: Will a large complex system be stable. Nature 238, 413–414 (1972)

    Article  Google Scholar 

  21. Mehta, M.L.: Random Matrices. Academic Press, New York (1967)

    MATH  Google Scholar 

  22. Wigner, E.P.: Gruppentheorie und Ihre Anwendung auf die Quantenmechanik der Atomspektren, trans. J. J. Griffin. Academic Press, New York (1959)

    Google Scholar 

  23. Sinha, S., Sinha, S.: Evidence of universality for the Wigner stability theorem for random networks with local dynamics. Phy. Rev. Let. E 71, 1–4 (2005)

    Google Scholar 

  24. Jirsa, V.K., Ding, M.: Will a large complex system with time delays be stable. Physical Review Letters 93, 70602 (2004)

    Article  Google Scholar 

  25. Ashby, W.R.: Design for a Brain. Chapman and Hall, London (1960)

    MATH  Google Scholar 

  26. Simon, H.A.: The Sciences of the Artificial. MIT Press, Cambridge (1969)

    Google Scholar 

  27. Tononi, G., Edelman, G., Sporns, O.: Complexity and coherency: integrating information in the brain. Trends in Cognitive Sciences 2, 474–483 (1998)

    Article  Google Scholar 

  28. Watson, R.A.: Modular interdependency in complex dynamical systems. In: Bilotta, E. (ed.) Workshop Proceedings of Alife VIII. MIT Press, Cambridge (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Buckley, C.L., Bullock, S., Cohen, N. (2005). Timescale and Stability in Adaptive Behaviour. In: Capcarrère, M.S., Freitas, A.A., Bentley, P.J., Johnson, C.G., Timmis, J. (eds) Advances in Artificial Life. ECAL 2005. Lecture Notes in Computer Science(), vol 3630. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11553090_30

Download citation

  • DOI: https://doi.org/10.1007/11553090_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28848-0

  • Online ISBN: 978-3-540-31816-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics