Hopf Bifurcation Analysis and Approximation of Limit Cycle in Coupled Van Der Pol and Duffing Oscillators
نویسندگان
چکیده
منابع مشابه
Double Hopf bifurcation in delayed van der Pol-Duffing equation
In this paper, we study dynamics in delayed van der Pol–Duffing equation, with particular attention focused on nonresonant double Hopf bifurcation. Both multiple time scales and center manifold reduction methods are applied to obtain the normal forms near a double Hopf critical point. A comparison between these two methods is given to show their equivalence. Bifurcations are classified in a two...
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Analysis and controlling of bifurcation for a class of chaotic Van der PolDuffing system with multiple unknown parameters are conducted. The stability of the equilibrium of the system is studied by using Routh-Hurwitz criterion, and the critical value of Hopf bifurcation is investigated. Based on the center manifold theory and normal form reduction, the stability index of bifurcation solution i...
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Analysis of numerical solutions for a system of two van der Pol–Duffing oscillators with nonlinear coupling showed that there exist chaotic switchings (occurring at irregular time intervals) between two oscillatory regimes differing by nearly time-constant phase shifts between the coupled subsystems. The analysis includes the investigation of bifurcations of the periodic motions corresponding t...
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Synchronization in the system of coupled non-identical nonisochronous Van fer Pol – Duffing oscillators with inertial and dissipative coupling is discussed. Generalized Adler’s equation is obtained and investigated in the presence of all relevant factors affecting the synchronization (nonisochronism of the oscillators, their nonidentity, coupling of the dissipative and inertial type). Character...
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The stability and bifurcation of a van der Pol-Duffing oscillator with the delay feedback are investigated, in which the strength of feedback control is a nonlinear function of delay. A geometrical method in conjunction with an analytical method is developed to identify the critical values for stability switches and Hopf bifurcations. The Hopf bifurcation curves and multi-stable regions are obt...
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ژورنال
عنوان ژورنال: The Open Acoustics Journal
سال: 2008
ISSN: 1874-8376
DOI: 10.2174/1874837600801010019