Abstract
The aim of the paper is to provide estimates of constants in the Fečkan Theorem and estimates guaranting pseudo orbit tracing property (POTP). These conditions constitute a theoretical foundation of weakly nonlinear neuron implementations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bielecki, A.: Dynamical properties of learning process of weakly nonlinear and nonlinear neurons, Nonlinear Analysis-Theory, Methods and Applications, Seria B: Real World Applications, vol. 2 (2001) 249–258
Jabłoński, D.: The conjugacy between cascades generated a perturbated linear system and the Euler method of a flow, Applicationes Mathematicae-accepted (2001)
Jabłoński, D., Bielecki, A.: Numerical conditions for the Feckan Theorem and applications to the artificial neural networks, Proceedings of the Sixth National Conference on ”Application of Mathematics in Biology and Medicine”, Zawoja (2000) 57–60
Fečkan, M.: The relation between a flow and its discretization. Math. Slovaca 42, no. 1 (1992), 123–127
Garay, B.: Discretization and some qualitative properties of ordinary differential equations about equilibria. Acta Math. Univ. Comenianae 62 (1993) 245–275
Ombach, J.: The simplest shadowing. Ann. Polon. Math. 58 (1993) 253–258
Palis, J., de Melo, W.: Geometric Theory of Dynamical Systems, Springer Verlag, New York (1982)
Reinfelds, A.: The shadowing lemma in a metric space. Univ. Iagel. Acta Math. 35 (1997) 205–210
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bielecki, A., Jabłoński, D. (2002). Estimation of Numerical Dynamics Constants of a Weakly Nonlinear Neuron. In: Wyrzykowski, R., Dongarra, J., Paprzycki, M., Waśniewski, J. (eds) Parallel Processing and Applied Mathematics. PPAM 2001. Lecture Notes in Computer Science, vol 2328. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48086-2_96
Download citation
DOI: https://doi.org/10.1007/3-540-48086-2_96
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43792-5
Online ISBN: 978-3-540-48086-0
eBook Packages: Springer Book Archive