AI Article Synopsis
- A new control method with time delayed coupling can alter stability features of systems near Hopf bifurcation.
- This method allows for an interchange between subcritical and supercritical Hopf bifurcations, helping stabilize both unstable periodic orbits and steady states.
- Numerical simulations of delay-coupled Van der Pol oscillators support the theoretical findings, highlighting effects like amplitude death and phase locking.
Article Abstract
We propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a Hopf bifurcation. We consider two delay-coupled normal forms for Hopf bifurcation and demonstrate the conversion of stability, i.e., an interchange between the sub- and supercritical Hopf bifurcation. The control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking. The main method and the results are applicable to a wide class of systems showing Hopf bifurcations, for example, the Van der Pol oscillator. The analytical theory is supported by numerical simulations of two delay-coupled Van der Pol oscillators, which show good agreement with the theory.
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| http://dx.doi.org/10.1103/PhysRevE.75.046206 | DOI Listing |
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