# What does Hopf mean?

## What does Hopf mean?

HOPF

Acronym Definition
HOPF Home Office Police Force (UK)

### 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.

#### Why do bifurcations occur?

Global bifurcations occur when ‘larger’ invariant sets, such as periodic orbits, collide with equilibria. This causes changes in the topology of the trajectories in the phase space which cannot be confined to a small neighbourhood, as is the case with local bifurcations.

What is a subcritical Hopf bifurcation?

When a stable limit cycle surrounds an unstable equilibrium point, the bifurcation is called asupercritical Hopf bifurcation. If the limit cycle is unstable and surrounds a stable equilibrium point, then the bifurcation is called a subcritical Hopf bifurcation(cf., p. 264).

What is Hopf bifurcation analysis in railway vehicles?

In railway vehicle systems, Hopf bifurcation analysis is notably important. Conventionally a railway vehicle’s stable motion at low speeds crosses over to unstable at high speeds.

## What is a complex conjugate bifurcation?

More accurately, it is a local bifurcation in which a fixed point of a dynamical system loses stability, as a pair of complex conjugate eigenvalues —of the linearization around the fixed point—crosses the complex plane imaginary axis.