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Analyzing of Hopf Bifurcation Based on Deterministic Learning

Danfeng Chen  Peng Lin  Cong Wang  
【摘要】:For parameter dependent nonlinear system, once the parameter reaches a critical point, the equivalent relationship of the system trajectory will be destroyed and further lead to structural instability of the whole system. This is the dynamic bifurcation phenomenon and is also the fundamental cause of instability oscillations and dynamic failures for most practical systems.In this research, Hopf bifurcation, the most common and typical dynamic bifurcation, will be discussed through deterministic learning theory. Firstly, an algebraic criterion of Hopf bifurcation is proposed according to the classical Hurwitz criterion, which provides a more convenient tool for Hopf bifurcation analyzing. Then, the bifurcation process with the change of system dynamics due to abnormal parameter variation is analyzed through deterministic learning. A C~1-norm based measure and negative exponential dynamic index are presented according to the structural stability theory, which can be used to analyze the steady state of current system. Finally, the classical Hodgkin-Hexley model is introduced to verify the feasibility and validity of the proposed algorithm.

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