Finding nondegenerate Hopf bifurcation points for four-dimensional two-parametric systems
نویسندگان
چکیده
منابع مشابه
Dynamical properties of chemical systems near Hopf bifurcation points.
In this paper, we numerically investigate local properties of dynamical systems close to a Hopf bifurcation instability. We focus on chemical systems and present an approach based on the theory of normal forms for determining numerical estimates of the limit cycle that branches off at the Hopf bifurcation point. For several numerically ill-conditioned examples taken from chemical kinetics, we c...
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Hopf bifurcations have been studied intensively in two dimensional vector fields with one slow and one fast variable [É. Benôıt et al., Collect. Math., 31 (1981), pp. 37–119; F. Dumortier and R. Roussarie, Mem. Amer. Math. Soc., 121 (577) (1996); W. Eckhaus, in Asymptotic Analysis II, Lecture Notes in Math. 985, Springer-Verlag, Berlin, 1983, pp. 449–494; M. Krupa and P. Szmolyan, SIAM J. Math....
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In this paper, we investigate the problem of bifurcation control for a delayed logistic growth model. By choosing the timedelay as the bifurcation parameter, we present a Proportional - Derivative (PD) Controller to control Hopf bifurcation. We show that the onset of Hopf bifurcation can be delayed or advanced via a PD Controller by setting proper controlling parameter. Under consideration mode...
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ژورنال
عنوان ژورنال: Computers & Mathematics with Applications
سال: 1997
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(97)00092-8