PBA.jar is a java program which lets you see the approximation of a PullBack random Attractor as it evolves in the phase space. It evolves the boundary of a specified deterministic set and waits a certain amount of time to see if it will collapse to a point. When the attractor has collapsed or the time is up it repeates the simulation with a different noise sample. Running the program for a long time produces an impression of the distribution of the collapsed random attractors. A simple Euler Maruyama scheme is used, hence the noise is assumed as Ito although this makes no difference for the additive noise systems given in the examples.

Collapsed attractors have their position recorded on the screen and printed out to a file temp.jpg. Below is an example of the distribution of collapsed attractors in a simulation of 5000 samples in the "Star" system.

Disc System Potential, additive noise Click here for applet demo of this system (uses lots of cpu!). X=(x,y) dX=-grad(V(X))*dt+sigma*dB_t B_t is 2 dimensional brownian motion. V(x,y) is the potential below.

Star System Potential, additive noise Click here for applet demo of this system (uses lots of cpu!). X=(x,y) dX=-grad(V(X))*dt+sigma*dB_t B_t is 2 dimensional brownian motion. V(x,y) is the potential below.