The Dynamical Systems Approach to Cognitive Science

Maurice Grinberg

Central and East European Centre for Cognitive Science

New Bulgarian University

 

Course description 

This course introduces the students to the dynamical systems theory and its use and influence in cognitive science. The basic concepts, terminology and methods of this approach will be presented and discussed from the general perspective of what a theory explaining the human cognitive processes should be. The presentation will be based on comparison with the symbolic and connectionist approaches.

During the afternoon sessions, several examples of models, taken from different fields of cognitive science, based on the dynamical systems approach will be discussed in detail.

1.   Theories and models in cognitive science: symbolic, connectionist and dynamical system approaches. Main requirements for a theory of cognition and the importance of models and simulations in cognitive science.

Readings:

  1. Port, R. F. & van Gelder, T. (eds.) (1995). It’s About Time: An Overview of the Dynamical Approach of Cognition. [html, excerpts][pdf]
    In Port, R. F. & van Gelder, T. (eds.)     (1995). Mind as Motion: Exploration in the Dynamics of Cognition. Cambridge, MA: MIT Press.
  2. van Gelder, T. J. (1999). Dynamic approaches to cognition. 
    In R. Wilson & F. Keil ed., The MIT Encyclopedia of Cognitive Sciences. Cambridge MA: MIT Press, 244-6. [pdf]
  3. Chapter 1: Representation and computation. In Thagard, P. (1996). Mind: Introduction to Cognitive Science. MA: MIT Press.
  4. Peschl, M. F. (2004). Cognition, Simulation, and Cognitive Science Constructing Knowledge and Synthesizing (Cognitive) Models. (in preparation)  
  5. van Gelder, T. J. (1998). The dynamical hypothesis in cognitive science. Behavioral and Brain Sciences, 21, 1-14. [pdf]
  6. Port, R. (in press). The dynamical systems hypothesis in cognitive science.  MacMillan Encyclopedia of Cognitive Science. Amy Lockyer, Assoc. Editor. [pdf]

2.   The dynamical system approach in cognitive science: The dynamical hypothesis. Comparison with the symbolic and connectionist approaches.

Readings:

  1. van Gelder, T. (1999) Revisiting the Dynamical Hypothesis. Preprint No. 2/99, University of Melbourne, Department of Philosophy. [pdf]
  2. Bates, E. A. & Elman, J. L. (2002). Connectionism And The Study Of Change. 
    In Mark Johnson (Ed.), Brain development and cognition: A reader (2nd ed.). Oxford: Blackwell Publishers. [pdf]
  3. Bechtel, W. (1997). Dynamics and Decomposition: Are They Compatible? Proceedings of the Australian Cognitive Science Society. [html]
  4. Bechtel, W. (1997). Representations and Cognitive Explanations: Assessing the Dynamicist's Challenge in Cognitive Science. Cognitive Science 22, 295-318 [html]
  5. French, R. M. & Thomas, E. (2001). The Dynamical Hypothesis in Cognitive Science: A review essay of Mind As Motion. Minds and Machines 11, 101-111.
  6. Beer, R.D. (2000). Dynamical approaches to cognitive science. Trends in Cognitive Sciences 4(3):91-99.
  7. Chapter 8: Review and evaluation and Dynamic Systems and  & Chapter 11: Mathematical Knowledge. In Thagard, P. (1996). Mind: Introduction to Cognitive Science. MA: MIT Press.              

3.   Introduction to the theory of dynamical systems. Phase space, trajectories, attractors, bifurcations. Example: the logistic map. Fractals and fractal dimension.

Readings:

  1. Chaos primer [http://www.societyforchaostheory.org/chaosprimer.pdf]
  2. Mandelbrodt and Julia sets [http://math.bu.edu/DYSYS/FRACGEOM/FRACGEOM.html]
  3. Chapter 1: Overview. In Strogatz, S. H. (1998). Nonlinear Dynamics and Chaos. USA: Westview, Perseus Books.
  4. Busemeyer, J. R. (2002) Dynamic Systems. Encyclopedia of Cognitive Science, Nadel, L. (Ed.) Nature. 1, 1039-1049.
  5. Chapter 9: Lorenz Equations. In Strogatz, S. H. (1998). Nonlinear Dynamics and Chaos. USA: Westview, Perseus Books.
  6. Software:
    1. Matlab based environment for nonlinear dynamics simulations [Matlab needed, rar]
    2. Game of  Life [http://www.bitstorm.org/gameoflife/]
    3. Attractors, fractals etc. [rar, runs under DOS]
  7. Chapter 11: Fractals. In Strogatz, S. H. (1998). Nonlinear Dynamics and Chaos. USA: Westview, Perseus Books.
  8. Chapter 12: Strange Attractors. In Strogatz, S. H. (1998). Nonlinear Dynamics and Chaos. USA: Westview, Perseus Books.

4.   Neural networks and the dynamical systems approach. Recurrent neural networks.

Readings:

  1. For ANN basics see Lecture#1[html]
  2. Chapters 1, 2, 7 and 15  in McLeod, P., Plunkett, K., & Rolls, E. T. (1998). Introduction to Connectionist Modelling of Cognitive Processes. UK: Oxford University Press.
  3. McClelland, J. L. & Rumelhart, D. E. (1981). An Interactive Activation Model of Context Effects in Letter Perception: Part 1. An Account of Basic Findings. Psych. Rev. 88, 357.
  4. Polack, J. (1995). The Induction of dynamical recognizers.[pdf] 
    In Port, R. F. & van Gelder, T. (eds.) (1995). Mind as Motion: Exploration in the Dynamics of Cognition. Cambridge, MA: MIT Press.

5.   Dynamic Systems Approach: Examples.

Readings:

  1. Townsend, J. T., & Busemeyer, J. (1995). Dynamic Representation of Decision-Making.[pdf] 
    In Port, R. F. & van Gelder, T. (eds.) (1995). Mind as Motion: Exploration in the Dynamics of Cognition. Cambridge, MA: MIT Press.
  2. Roe, R. M., Busemeyer, J. R., & Townsend, J. T. (2001). Multi-alternative decision field theory: A dynamic connectionist model of decision making. Psychological Review 108, 370-392. [pdf]
  3. Elman, J. L. Chapter 8: Language as a Dynamical System. 
    In Port, R. F. & van Gelder, T. (eds.) (1995). Mind as Motion: Exploration in the Dynamics of Cognition. Cambridge, MA: MIT Press. [pdf] 
  4. van Geert, P. Chapter 11: Growth Dynamics in Development.
    In Port, R. F. & van Gelder, T. (eds.) (1995). Mind as Motion: Exploration in the Dynamics of Cognition. Cambridge, MA: MIT Press.
  5. Freeman, W. J. (1991). The Physiology of Perception. Scientific American 264, 78-85. [html]
  6. Skarfda, C. A. & Freeman, W. J. (1987). How brains make chaos in order to make sense of the world. Behavioral and Brain Sciences 10, 161–195 [html]
  7. West, R. L. & Lebiere, C. (2001). Simple games as dynamic, coupled systems: randomness and other emergent properties. Cognitive Systems Research 1(4), 221-239. [pdf]
  8. Macy, M. W. & Flache, A. (2002). Learning dynamics in social dilemmas. PNAS 99, Suppl. 3, 7229-7236

 

During the afternoon sessions, the students will be asked to write short critical essays on the discussed papers and to present and defend their own ideas on the topics considered. The final essay should be a generalization of these short essays and is expected to display the personal position of the students based on the knowledge acquired during the course.

 

 

Maurice Grinberg

 

Maurice Grinberg (http://www.nbu.bg/cogs/cvs/greenb.html) is Associate Professor in the Central and Easte European Center for Cognitive Science, at the New Bulgarian University. His research interests arein the field of cognitive modeling, decision making, experimental economics.