Abstract
An SMIB model in the power systems, especially that concering the effects of hard limits on bifurcations, chaos and stability is studied. Parameter conditions for bifurcations and chaos in the absence of hard limits are compared with those in the presence of hard limits. It has been proved that hard limits can affect system stability. We find that (1) hard limits can change unstable equilibrium into stable one; (2) hard limits can change stability of limit cycles induced by Hopf bifurcation; (3) persistence of hard limits can stabilize divergent trajectory to a stable equilibrium or limit cycle; (4) Hopf bifurcation occurs before SN bifurcation, so the system collapse can be controlled before Hopf bifurcation occurs. We also find that suitable limiting values of hard limits can enlarge the feasibility region. These results are based on theoretical analysis and numerical simulations, such as condition for SNB and Hopf bifurcation, bifurcation diagram, trajectories, Lyapunov exponent, Floquet multipliers, dimension of attractor and so on.
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Supported by The National Key Basic Research Fundation (No. G1998020307).
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Wang, Rq., Huang, Jc. Effects of Hard Limits on Bifurcation, Chaos and Stability. Acta Mathematicae Applicatae Sinica, English Series 20, 441–456 (2004). https://doi.org/10.1007/s10255-004-0183-x
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DOI: https://doi.org/10.1007/s10255-004-0183-x