منابع مشابه
MULTIVALUED p-LIENARD SYSTEMS
In the last decade, there have been many papers dealing with second-order multivalued boundary value problems. We mention the works of Erbe and Krawcewicz [5, 6], Frigon [7, 8], Halidias and Papageorgiou [9], Kandilakis and Papageorgiou [11], Kyritsi et al. [12], Palmucci and Papalini [17], and Pruszko [19]. In all the above works, with the exception of Kyritsi et al. [12], p = 2 (linear differ...
متن کاملGeneralized Liénard Equations, Cyclicity and Hopf–Takens Bifurcations
We investigate the bifurcation of small–amplitude limit cycles in generalized Liénard equations. We use the simplicity of the Liénard family, to illustrate the advantages of the approach based on Bautin ideals. Essentially, this Bautin ideal is generated by the so–called Lyapunov quantities, that are computed for generalized Liénard equations and used to detect the presence of a Hopf– Takens bi...
متن کاملRenormalization group and Lienard systems of differential equations
Autonomous Lienard systems, which constitute a huge family of periodic motions, exhibit limit cycle behaviour in certain cases and centres in others. In the literature, the signature for the existence of these two different facets of periodic behaviour has been studied from different geometrical perspectives and not from a general viewpoint. Starting out from general considerations, we show in ...
متن کاملHopf Bifurcation in Numerical Approximation for the Generalized Lienard Equation with Finite Delay
The numerical approximation of the generalized Lienard equation is considered using delay as parameter. First, the delay difference equation obtained by using Euler method is written as a map.According to the theories of bifurcation for discrete dynamical systems,the conditions to guarantee the existence of Hopf bifurcation for numerical approximation are given. The relations of Hopf bifurcatio...
متن کاملDiscretizing Dynamical Systems with Hopf-Hopf Bifurcations
We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that Hopf-Hopf bifurcations are O(h)-shifted and turned into double Neimark-Sacker points by general one-step methods of order p. Then we discuss the effect of discretization methods on the emanating Hopf curves. The numerical approximation of the critical eigenvalues is analyzed too. The resul...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2001
ISSN: 0893-9659
DOI: 10.1016/s0893-9659(00)00133-6