sim_fun_grad: A simple gradient simulation function for testing

In simlandr: Simulation-Based Landscape Construction for Dynamical Systems

A simple gradient simulation function for testing

Description

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 + σ dW/dt = - 4x^3 - ay - b + σ dW/dt

dy/dt = - \partial U/ \partial y + σ dW/dt = - 4y^3 - ax - c + σ dW/dt

Usage

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 σ 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.

See Also

sim_fun_nongrad() and batch_simulation().

simlandr documentation built on Nov. 16, 2022, 1:12 a.m.