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Discrete Liapunov functions with Δ2V>0

Published online by Cambridge University Press:  17 February 2009

Phil Diamond
Phil Diamond
Affiliation:
Department of Mathematics, University of Queensland, St Lucia, Qld, Australia, 4067
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Abstract

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Consideration of functions whose second difference along the trajectories of a difference equation is positive gives a stability theorem for autonomous discrete-time systems. Such functions can be used to estimate domains of nonglobal stability.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 3 , June 1978 , pp. 280 - 284
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Chow, S. and Dunninger, D. R., ‘Lyapunov functions satisfying V> 0’, SIAM. J. Appl. Math. 26 (1974), 165–168.CrossRefGoogle Scholar
[2]Yorke, J. A., ‘A theorem on Liapunov functions using V’, Math. Systems Theory 4 (1970), 40–45.CrossRefGoogle Scholar
[3]Diamond, P., ‘Domains of stability and resilience for biological populations obeying difference equations’, J. Theor. Biol. 61 (1976), 287–306.CrossRefGoogle ScholarPubMed