What do you mean by Hopf bifurcation?
The term Hopf bifurcation (also sometimes called Poincaré-Andronov-Hopf bifurcation) refers to the local birth or death of a periodic solution (self-excited oscillation) from an equilibrium as a parameter crosses a critical value.
What is supercritical bifurcation?
In the supercritical pitch- fork, a stable fixed point becomes unstable at the bifurcation point, but two other stable fixed points are generated, as seen. The subcritical pitchfork is the same except for a sign change in all the growth rates.
What is neimark Sacker bifurcation?
Neimark-Sacker bifurcation is the birth of a closed invariant curve from a fixed point in dynamical systems with discrete time (iterated maps), when the fixed point changes stability via a pair of complex eigenvalues with unit modulus.
Who discovered the Hopf bifurcation?
Yuri A. Kuznetsov
Yuri A. Kuznetsov (2006), Scholarpedia, 1(10):1858. Figure 1: Supercritical Andronov-Hopf bifurcation in the plane.
What is subcritical Hopf bifurcation?
When a stable limit cycle surrounds an unstable equilibrium point, the bifurcation is called a supercritical Hopf bifurcation. If the limit cycle is unstable and surrounds a stable equilibrium point, then the bifurcation is called a subcritical Hopf bifurcation (cf. [3], p. 264).
What is a bifurcation value?
A bifurcation of a dynamical system occurs when the parameter value of a system changes such that it causes a sudden qualitative change in its behaviour. Bifurcations occur in both continuous systems and discrete sys- tems.
What is imperfect bifurcation?
Abstract. Imperfect bifurcation phenomena are formulated in framework of analytical bifurcation theory on Banach spaces. In particular the perturbations of transcritical and pitchfork bifurcations at a simple eigenvalue are examined, and two-parameter unfoldings of singularities are rigorously established.
What does Hopf mean?
German: metonymic occupational name for a grower of hops or dealer in hops, or a metonymic occupational name for a brewer, from the use of hops in the manufacture of beer, from Middle High German hopfe ‘hops’.
What is a subcritical Hopf bifurcation?
What is Matcont?
MATCONT is a graphical MATLAB software package for the interactive numerical study of dynamical systems. It allows one to compute curves of equilibria, limit points, Hopf points, limit cycles, period doubling bifurcation points of limit cycles, and fold bifurcation points of limit cycles.