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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Eric Kendel and James H. Schwartz, Principles of Neural Science, Elsevier, New York, 1985.
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.
J. R. Munkres, Topology, Prentice Hall, Engelwood Cliffs, N.J., 1975
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.
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.
Editor information
Editors and Affiliations
Additional information
Dedicated to Professor Antonio Ruberti on the occasion of his 65th birthday
Rights and permissions
Copyright information
© 1992 Springer Science+Business Media New York
About this chapter
Cite this chapter
Brockett, R.W. (1992). Pulse Driven Dynamical Systems. In: Isidori, A., Tarn, TJ. (eds) Systems, Models and Feedback: Theory and Applications. Progress in Systems and Control Theory, vol 12. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-2204-8_7
Download citation
DOI: https://doi.org/10.1007/978-1-4757-2204-8_7
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4757-2206-2
Online ISBN: 978-1-4757-2204-8
eBook Packages: Springer Book Archive