I am able to reproduce Pyragas' results from his 1992 paper for the Rössler system operating in the spiral regime (e.g. a=0.2, b=0.2 and c=5.7). However, it has been much harder to find situations where an UPO of that system operating in the funnel regime (e.g. a=0.28, b=0.1 and c=8.5) is stabilized using Pyragas' delay control law. I am able to stabilize period-one UPOs but have not found UPOs with longer periods yet. Has anyone information (references) on this problem?
Thank you in advance.
Thank you all for reading and considering answering to my question posted on June 20th. As far as I can tell, there seems to be no evidence that Pyragas' delay method works for the Rössler system operating in the funnel (phase noncoherent) regime. If anyone knows of a successful example or has any clue as to why it doesn't work, please let me know.
I have tried Pyragas' second method, the one that uses a given UPO as reference to stabilize such an orbit applying the linear and dissipative control action
u=K(y_upo - y_system).
This method works very well even with the Rössler system operating in the funnel regime.
Regards to all.
Thanks Andreas. The Rossler system even in the funnel regime is just chaotic, not hyperchaotic. Thank you for your tip on multiple-delay feedback.
Cheers.
I have just posted scripts that implement Pyragas' methods. In case you are interested, you can find them at: https://www.researchgate.net/project/Scripts-on-Nonlinear-Dynamics
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