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.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Kauffman, S.: The Origins of Order. Oxford University Press, Oxford (1993)
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)
Beer, R.D.: On the dynamics of small continuous-time recurrent neural networks. Adaptive Behavior 3, 471–511 (1995)
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)
Poggio, T.A., Glaser, D.A. (eds.): Exploring Brain Functions: Models in Neuro- science. John Wiley and Sons, New York (1993)
Katz, P.S. (ed.): Beyond Neurotransmission: Neuromodulation and its Importance for Information Processing. Oxford University Press, Oxford (1999)
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)
Doya, K.: Metalearning and neuromodulation. Neural Networks 15, 495–506 (2002)
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)
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., SosÃk, P. (eds.) ECAL 2001. LNCS (LNAI), vol. 2159, pp. 23–36. Springer, Heidelberg (2001)
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)
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)
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)
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)
Hooper, S.L.: Neural circuits: Functional reconfiguration. In: Nature Encyclopedia of Life Science. Nature Publishing Group, London (2001)
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)
Strogatz, S.H.: Nonlinear Dynamics & Chaos. Addison-Wesley, Reading (1994)
Gardner, M.R., Ashby, W.R.: Connectance of large dynamic (cybernetic) systems: Critical values for stability. Nature 228, 784–784 (1970)
McCann, K.S.: The diversity-stability debate. Nature 405, 228–233 (2000)
May, R.M.: Will a large complex system be stable. Nature 238, 413–414 (1972)
Mehta, M.L.: Random Matrices. Academic Press, New York (1967)
Wigner, E.P.: Gruppentheorie und Ihre Anwendung auf die Quantenmechanik der Atomspektren, trans. J. J. Griffin. Academic Press, New York (1959)
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)
Jirsa, V.K., Ding, M.: Will a large complex system with time delays be stable. Physical Review Letters 93, 70602 (2004)
Ashby, W.R.: Design for a Brain. Chapman and Hall, London (1960)
Simon, H.A.: The Sciences of the Artificial. MIT Press, Cambridge (1969)
Tononi, G., Edelman, G., Sporns, O.: Complexity and coherency: integrating information in the brain. Trends in Cognitive Sciences 2, 474–483 (1998)
Watson, R.A.: Modular interdependency in complex dynamical systems. In: Bilotta, E. (ed.) Workshop Proceedings of Alife VIII. MIT Press, Cambridge (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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)