Robertson, S., Cohen, A., and Mayer-Kress, G. (1993). Behavioral chaos: Behind the metaphor. In Smith, L. and Thelen, E., editors, A Dynamic Systems Approach to Development: Applications, pages 119--150. Bradford/MIT Press, Cambridge, Mass.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... (e.g. Jaeger and Christaller, 1998) Large et al. 1997) recurrent neural networks (e.g. Beer, 1995) and stochastic automata (e.g. Baasye et al. 1995) The most common kind of formal analyis concerns the description of attractor structures emerging from learning or evolution (e.g. (Robertson et al. 1993)(Smithers, 1995) In the present article I wish to point out a basic property of dynamical systems based robots, namely, the inherent multifunctionality of input driven dynamical systems. I shall demonstrate the ubiquity of this property, and discuss the di#culties as well as the chances that it ....

Robertson, S., Cohen, A., and Mayer-Kress, G. (1993). Behavioral chaos: Behind the metaphor. In Smith, L. and Thelen, E., editors, A Dynamic Systems Approach to Development: Applications, pages 119--150. Bradford/MIT Press, Cambridge, Mass.

....in dimensionality is the slaving principle [3] This topic deserves a more detailed discussion than is possible here. Let me only mention that motor action patterns involving many dozens of muscular and joint df s have been described in terms of low dimensional systems in human psychophysics [8] [7]. DD target dynamics makes use of this potential for simplification by generating g(t) in two steps. In the first step, a low dimensional dynamical system produces a target representation trajectory x(t) from which the high dimensional target trajectory that regulates the effectors is computed ....

S.S. Robertson, A.H. Cohen, and G. Mayer-Kress. Behavioral chaos: Behind the metaphor. In L.B. Smith and E. Thelen, editors, A Dynamic Systems Approach to Development: Applications, pages 119--150. Bradford/MIT Press, Cambridge, Mass., 1993.

....for in the dynamics of variables that belong to the dynamical systems of both the agent and its environment, i.e. that belong to the interaction space . One should also mention research in psychophysics where observed motor behavior patterns are formally reconstructed as attractors (e.g. 22] [20]) With the exception of [23] where the perspective is still too abstract for yielding concrete criteria for identifying behaviors, these contributions concern the description of single behaviors. An essential tacit assumption is that an isolated behavior can be exhibited and observed for a long ....

....shows how several formal, logical requirements for such inferences are satisfied by neural network mechanisms. Last but not least, there are several strands of work in psychophysics and behavior oriented robotics where motor behaviors are modeled by attractors. I have already mentioned these [22][20][27] 21] 5] in the introduction. Limit cycles and chaotic attractors, too, have been identified with concepts, perceptual categories, and representations of motor programs. This view is common in recent work on biologically inspired, artificial neural networks (e.g. 7] and on neural network ....

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S.S. Robertson, A.H. Cohen, and G. Mayer-Kress. Behavioral chaos: Behind the metaphor. In L.B. Smith and E. Thelen, editors, A Dynamic Systems Approach to Development: Applications, pages 119--150. Bradford/MIT Press, Cambridge, Mass., 1993.

.... modeling of neural cognitive phenomena, basically because identifying a high dimensional chaotic attractor in an empirical time series typically requires more data than can be gathered while the attractor is extant (for more detailed criticism, cf. 47] 43] for an enlightening case study cf. [48]) I am afraid that in live brains under real life conditions, chaotic attractors cannot be monitored long and or precisely enough to certify their existence. I would stick out my neck even further and question that chaotic attractors are the right mathematical metaphor at all for what we would ....

S.S. Robertson, A.H. Cohen, and G. Mayer-Kress. Behavioral chaos: Behind the metaphor. In L.B. Smith and E. Thelen, editors, A Dynamic Systems Approach to Development: Applications, pages 119--150. Bradford /MIT Press, Cambridge, Mass., 1993.

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