QUERY First order oscillation
Posted: Fri Jun 01, 2007 1:11 pm
Posted by ""Welch, Cory"" <Cory_Welch@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@nrel.gov> posting date Thu, 31 May 2007 10:06:46 -0600 _______________________________________________
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@nrel.gov> posting date Thu, 31 May 2007 10:06:46 -0600 _______________________________________________