phase portrait

The small graph above the pendulums are their phase portraits.

Next he plots both components in a diagram, thus creating an experimental phase portrait.

Other techniques may be used to find (exact) phase portraits and approximate periods.

Phase portraits are an invaluable tool in studying dynamical systems.

The image below shows a phase portrait before, at, and after a homoclinic bifurcation in 2D.

Its phase portrait is a simple circle .

File: Phase portrait center.

It can be clearly seen on the phase portrait of the basic system of equations describing the active medium (see Fig.)

Phase portrait solutions for the continuous linear-fitness replicator equation have been classified in the two and three dimensional cases.

The phase portrait illustrating the Hopf bifurcation in the Selkov model is shown on the right.

Increasing the amplitude of driving oscillations to half of the pendulum length leads to the phase portrait shown in the figure.

The set of all phase paths, i.e. general solution to the differential equations, is the phase portrait:

Simple harmonic oscillator where the phase portrait is made up of ellipses centred at the origin, which is a fixed point.

A phase portrait is a geometric representation of the trajectories of a dynamical system in the phase plane.

Instead of solving the system analytically which can be difficult for many functions, it is often best to take a geometric approach and draw a phase portrait.

File: Phase Portrait Sadle.

The detailed analysis shows that there are 23 different phase portraits for this sytem, including oscillations, multiplicity of steady states and various types of bifurcations.

A phase portrait is a qualitative sketch of the differential equation's behavior that shows equilibrium solutions or fixed points and the vector field on the real line.

The concept of topological equivalence is important in classifying the behaviour of systems by specifying when two different phase portraits represent the same qualitative dynamic behavior.

Interesting phase portraits might be obtained in regimes which are not accessible within analytic descriptions, for example in the case of large amplitude of the suspension .

The entire field is the phase portrait, a particular path taken along a flow line (i.e. a path always tangent to the vectors) is a phase path.

In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points.

The topological changes in the phase portrait of the system can be confined to arbitrarily small neighbourhoods of the bifurcating fixed points by moving the bifurcation parameter close to the bifurcation point (hence 'local').

In this case, a sketch of the phase portrait may give qualitative information about the dynamics of the system, such as the limit cycle of the Van der Pol oscillator shown in the diagram.