Pulse Driven Dynamical Systems

  • R. W. Brockett
Chapter
Part of the Progress in Systems and Control Theory book series (PSCT, volume 12)

Abstract

Implicit in much of the ongoing work in neural computing is the contention under certain circumstances it is useful to think about computer programs and/or computing hardware in terms of analog processing rather than insisting on a digital point of view. The arguments that have been advanced thus far are largely inconclusive, in part because there is no readily applicable formal basis for such studies. In this note we suggest a topological method for organizing the input/output analysis of dynamical systems in such a way as to facilitate comparisons of this type.

Keywords

Equivalence Class Equilibrium Point Differential Inclusion Connected Open Subset Mathematical System Theory 
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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References

  1. [1]
    Eric Kendel and James H. Schwartz, Principles of Neural Science, Elsevier, New York, 1985.Google Scholar
  2. [2]
    A. F. Murray et al., “Pulsed Silicon Neural Networks-Following the Biological Leader”, in VLSI Design of Neural Networks, U. Ramacher, U. Ruckert, Eds., Kluwer Academic Publisher, Boston, 1991.Google Scholar
  3. [3]
    J. R. Munkres, Topology, Prentice Hall, Engelwood Cliffs, N.J., 1975Google Scholar
  4. [4]
    R.W. Brockett, Smooth Dynamical Systems Which Realize Arithmetical and Logical Operations, in Lecture Notes in Control and Information Sciences. Three Decades of Mathematical Systems Theory. (H. Nijmeijer and J. M. Schumacher, eds.) Springer-Verlag, Berlin, 1989, pp. 19–30.Google Scholar
  5. [5]
    R. W. Brockett, “On the Asymptotic Properties of Solutions of Differential Equations with Multiple Equilibria,” Journal of Di f ferential Equations, Vol. 18 (1982) pp. 249–262.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • R. W. Brockett

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