QUERY First order oscillation (SD6459)

[SDMAIL Welch, Cory]

Posted by  "Welch, Cory" <Cory_Welch at nrel.gov>

I am currently engaged in a debate regarding continuous-time vs.
discrete-time modeling. As a result, I came across two articles that
claim a first order difference equation (they use the logistic equation
as an example) is capable of a) oscillation, and b) chaotic behavior. As
any good system dynamicist knows, this is of course impossible. These
articles are referenced countless times in ecology literature. 

At first glance, it seems to me that the articles are mistakenly
interpreting instability resulting from using discrete time rather than
continuous time as "true" oscillation. 

First, I am wondering whether I am correct in my interpretation. 

Second, I wonder anyone on this list knows of a published rebuttal
specific to the contentions set forth in these articles (I am aware of
the discussion on oscillation in Business Dynamics). 

Finally, if anyone can point me toward publications regarding the merits
of continuous-time vs. discrete time modeling, it would be greatly
appreciated. 

Best regards,

Cory Welch

Articles referred to above:
Robert M. May "Simple mathematical models with very complicated
dynamics" Nature, Vol 261, June 10, 1976, pp. 459-467.

Robert M. May, George F. Oster "Bifurcations and Dynamic Complexity in
Simple Ecological Models" The American Naturalist, Vol. 110, No. 974
(Jul. - Aug., 1976), pp. 573-599




Cory J. Welch
Senior Energy Analyst
National Renewable Energy Laboratory
    Strategic Energy Analysis and Applications Center
Posted by  "Welch, Cory" <Cory_Welch at nrel.gov>
posting date  Thu, 31 May 2007 10:06:46 -0600