TU Berlin

Institute of Theoretical PhysicsOdd-Number Limitation

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C++ visualisation for the Odd-Number Limitation

This program simulates the behavior of a subcritical Stuart-Landau oscillator in the uncontrolled case, in case of "delayed feedback control" and "extended delayed feedback control". The control signals complex amplitude and radius of the oscillator are presented in dependence of the systems time. Additionally phase-space trajectories are presented to the user for any of the three cases.
The system has an odd number of Floquet multipliers. Hence, according to the in 2007 refuted odd-number limitation [1,2], a stabilization of the uncontrolled systems unstable limit cycle should be impossible if using the mentioned control methods.
The user is provided with analytically determined parameter spaces, for which the behavior of the system will contradict to the odd-number limitation. The refutation of the odd-number limitation can be reproduced numerically by running the program with a set of parameters from this spaces.


Underlying system of differential equations



[1] B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, and E. Schöll: Refuting the odd number limitation of time-delayed feedback control, Phys. Rev. Lett. 98, 114101 (2007)

[2] H. Nakajima: On analytical properties of delayed feedback control of chaos, Phys. Lett. A 232, 207 (1997).


Documentation (Only a german version is currently available)

Program for usage at Windows operating systems with graphical user-interface and provided as executable file

Attention: The Microsoft.NET Framework 4.5.1 or higher is required to run the program.


Program for usage at all operating systems as terminal application


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