This simulation illustrates the concept of a limit cycle by using the following mathematical model:

dx/dt = y +  [K*x*(1 - x^2 - y^2)]/sqrt(x^2 +  y^2)

dy/dt = -x + [K*y*(1 - x^2 - y^2)]/sqrt(x^2 +  y^2)

The initial conditions are as follows:

x(0) = x0

y(0) = y0

The limit cycle of this function is a circle centered at the origin with radius 1 (the unit circle), which can be expressed in the following statement.

For all x0,y0 (where x0, y0 are non-zero), x^2 + y^2 approaches 1 as t tends to infinity.