This is a toy stochastic gradient system which can have bistability in some conditions. Model specification: $$U = x^4 + y^4 + axy + bx + cy$$ $$dx/dt = - \partial U/ \partial x + \sigma dW/dt = - 4x^3 - ay - b + \sigma dW/dt$$ $$dy/dt = - \partial U/ \partial y + \sigma dW/dt = - 4y^3 - ax - c + \sigma dW/dt$$
Two sets of parameters.
initial contains the initial value of
a,b,c, which control the shape of the potential landscape,
sigmasq, which is the square of \(\sigma\) and controls the amplitude of noise.
The length of simulation.
The step size used in the Euler method.
The initial seed that will be passed to
A matrix of simulation results.