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...

bifurcation Pitchfork bifurcation Period-doubling (flip) bifurcation Hopf bifurcation Neimark–Sacker (secondary Hopf) bifurcation Global bifurcations...

for by the bifurcation theory. As the carrying capacity increases, the equilibrium of the dynamical system becomes unstable. The bifurcation can be obtained...

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...

In bifurcation theory, a field within mathematics, a pitchfork bifurcation is a particular type of local bifurcation where the system transitions from...

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...

context of a biological system, bifurcation theory describes how small changes in an input parameter can cause a bifurcation or qualitative change in the...

increasing rate Hopf bifurcation, in mathematics, a local bifurcation; when the first Lyapunov coefficient is negative, the bifurcation is called supercritical...

codimension-one bifurcations occur nearby: a saddle-node bifurcation, an Andronov–Hopf bifurcation and a homoclinic bifurcation. All associated bifurcation curves...

mathematical area of bifurcation theory a saddle-node bifurcation, tangential bifurcation or fold bifurcation is a local bifurcation in which two fixed...