REPLY First order oscillation (SD6463)

[SDMAIL Scott Rockart]

Posted by  Scott Rockart <srockart at duke.edu>

Hi Cory,

Tu (Dynamical Systems, 2nd edition 1994, Springer-Verlag) has a nice concise discussion 
of limit cycles and chaotic behavior in difference and differential equations which 
makes specific use of the logistic equation as an example (see section 10.3).  His 
discussion supports rather than refutes the conclusions that both oscillation and chaos 
are possible in the first order difference equations, but notes that continuous 
functions must be at least second order for limit cycles and third order for chaos.  
Sterman makes similar points (omitting proofs) on page 290 of Business Dynamics (see 
footnote).  In light of that, the debate seems to be whether and when the behavior of 
the difference equations reflect the behavior of the systems of interest rather than 
merely reflecting integration errors.

Best,

Scott 
Posted by  Scott Rockart <srockart at duke.edu>
posting date  Fri, 01 Jun 2007 16:17:34 -0400