In the mathematical theory of bifurcations, a Hopf bifurcation is a critical point where, as a parameter changes, a system's stability switches and a periodic...
21 KB (3,707 words) - 03:37, 8 April 2024
bifurcation Pitchfork bifurcation Period-doubling (flip) bifurcation Hopf bifurcation Neimark–Sacker (secondary Hopf) bifurcation Global bifurcations...
16 KB (1,855 words) - 17:14, 2 April 2024
In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from...
3 KB (506 words) - 03:21, 7 May 2024
Van der Pol oscillator (section Hopf bifurcation)
Hopf bifurcation, the limit cycle should have size ∝ ε 1 / 2 , {\displaystyle \propto \varepsilon ^{1/2},} we may attempt to convert this to a Hopf bifurcation...
21 KB (2,631 words) - 08:16, 30 September 2024
for by the bifurcation theory. As the carrying capacity increases, the equilibrium of the dynamical system becomes unstable. The bifurcation can be obtained...
10 KB (1,524 words) - 20:34, 6 February 2024
variables. Another example shows how a center manifold models the Hopf bifurcation that occurs for parameter a ≈ 4 {\displaystyle a\approx 4} in the delay...
18 KB (2,574 words) - 15:53, 14 February 2024
mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed...
6 KB (805 words) - 06:14, 22 March 2024
context of a biological system, bifurcation theory describes how small changes in an input parameter can cause a bifurcation or qualitative change in the...
19 KB (2,558 words) - 17:39, 18 June 2024
Hodgkin–Huxley model (section Bifurcations)
{\displaystyle I} were used as a bifurcation parameter, then the Hodgkin–Huxley model undergoes a Hopf bifurcation. As with most neuronal models, increasing...
21 KB (3,045 words) - 04:15, 1 August 2024
increasing rate Hopf bifurcation, in mathematics, a local bifurcation; when the first Lyapunov coefficient is negative, the bifurcation is called supercritical...
2 KB (249 words) - 03:34, 29 August 2020