This is a toy stochastic gradient system which can have bistability in some conditions.
Model specification:
$$U = x^4 + y^4 + axy + bx + cy$$
$$dx/dt = - \partial U/ \partial x + \sigma dW/dt = - 4x^3 - ay - b + \sigma dW/dt$$
$$dy/dt = - \partial U/ \partial y + \sigma dW/dt = - 4y^3 - ax - c + \sigma dW/dt$$

```
sim_fun_grad(
initial = list(x = 0, y = 0),
parameter = list(a = -4, b = 0, c = 0, sigmasq = 1),
length = 1e+05,
stepsize = 0.01,
seed = NULL
)
```

## Arguments

- initial, parameter
Two sets of parameters. `initial`

contains the initial value of `x`

and `y`

;
`parameter`

contains `a,b,c`

, which control the shape of the potential landscape,
and `sigmasq`

, which is the square of \(\sigma\) and controls the amplitude of noise.

- length
The length of simulation.

- stepsize
The step size used in the Euler method.

- seed
The initial seed that will be passed to `set.seed()`

function.

## Value

A matrix of simulation results.