What is functional bifurcation?
In mathematics, particularly in dynamical systems, a bifurcation diagram shows the values visited or approached asymptotically (fixed points, periodic orbits, or chaotic attractors) of a system as a function of a bifurcation parameter in the system.
What is local bifurcation?
Local bifurcations A local bifurcation occurs when a parameter change causes the stability of an equilibrium (or fixed point) to change. If the eigenvalue is equal to one, the bifurcation is either a saddle-node (often called fold bifurcation in maps), transcritical or pitchfork bifurcation.
What is bifurcation chaos?
The appearance of chaos in a system is usually associated with systems whose mathematical model has a parameter that can vary. For a given range of values of this parameter, the system will exhibit a chaotic behavior. The point that marks this change is called a bifurcation point.
What is a cusp bifurcation?
The cusp bifurcation is a bifurcation of equilibria in a two-parameter family of autonomous ODEs at which the critical equilibrium has one zero eigenvalue and the quadratic coefficient for the saddle-node bifurcation vanishes.
What is called period-doubling?
A period-doubling bifurcation corresponds to the creation or destruction of a periodic orbit with double the period of the original orbit.
What is a bifurcation value?
An equilibrium can become unstable and a periodic solution may appear or a new stable equilibrium may appear making the previous equilibrium unstable. The value of parameter at which these changes occur is known as ”bifurcation value” and the parameter that is varied is known as the ”bifurcation parameter”.
What does bifurcate mean in medical terms?
[bi-fur-ka´shun] 1. a division into two branches, such as a blood vessel, or a tooth that has two roots. Bifurcatio aortae (aortic bifurcation), showing the branching of the abdominal aorta into the common iliac arteries, and from there to the internal and external iliac arteries.
What is a non-transversal homoclinic bifurcation?
The homoclinic structure appears/disappears via a non-transversal homoclinic bifurcation, when the stable and the unstable manifolds of the fixed point become tangent along the homoclinic orbit [a3], [a4], [a16] . N.K. Gavrilov, L.P. Shilnikov, “On three-dimensional systems close to systems with a structurally unstable homoclinic curve: I” Mat.
When does a limit cycle bifurcate?
If the saddle-node has a single homoclinic orbit $ \\Gamma _ {0} $, then, generically, a unique limit cycle bifurcates from $ \\Gamma _ {0} $, when the saddle-node disappears via the fold bifurcation. The cycle can be either attracting/repelling or saddle type, depending on the location of the non-zero eigenvalues of $ x _ {0} $ on the complex plane.
What is the bifurcation of the apophyses?
Bifurcation: a forking or division into two: the point at which a forking occurs. The bifurcation at the pasterns, and the two larger pasterns to each foot. But in other species the ramification of the apophyses assumes more the form of bifurcation or of irregular branching.
What does bifurcation mean in geography?
Bifurcation: a forking or division into two: the point at which a forking occurs. The bifurcation at the pasterns, and the two larger pasterns to each foot.
