sim_fun_nongrad: A simple non-gradient simulation function for testing

In simlandr: Simulation-Based Landscape Construction for Dynamical Systems

A simple non-gradient simulation function for testing

Description

This is a toy stochastic non-gradient system which can have multistability in some conditions. Model specification:

Usage

sim_fun_nongrad(
  initial = list(x1 = 0, x2 = 0, a = 1),
  parameter = list(b = 1, k = 1, S = 0.5, n = 4, lambda = 0.01, sigmasq1 = 8, sigmasq2 =
    8, sigmasq3 = 2),
  constrain_a = TRUE,
  amin = -0.3,
  amax = 1.8,
  length = 1e+05,
  stepsize = 0.01,
  seed = NULL,
  progress = TRUE
)

Arguments

initial, parameter	Two sets of parameters. initial contains the initial value of x1, x2, and a; parameter contains ⁠b,k,S,n,lambda⁠, which control the model dynamics, and ⁠sigmasq1,sigmasq2,sigmasq3⁠, which are the squares of \sigma_1,\sigma_2,\sigma_3 and controls the amplitude of noise.
constrain_a	Should the value of a be constrained? (TRUE by default).
amin, amax	If constrain_a, the minimum and maximum values of a.
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.
progress	Show progress bar of the simulation?

Details

\frac {dx_ {1}}{dt} = \frac {ax_ {1}^ {n}}{S^ {n}+x_ {1}^ {n}} + \frac {bS^ {n}}{S^ {n}+x_ {2}^ {n}} - kx_ {1}+ \sigma_1 dW_1/dt

\frac {dx_ {2}}{dt} = \frac {ax_ {2}^ {n}}{S^ {n}+x_ {2}^ {n}} + \frac {bS^ {n}}{S^ {n}+x_ {1}^ {n}} - kx_ {2}+ \sigma_2 dW_2/dt

\frac {da}{dt} = -\lambda a+ \sigma_3 dW_3/dt

Value

A matrix of simulation results.

References

Wang, J., Zhang, K., Xu, L., & Wang, E. (2011). Quantifying the Waddington landscape and biological paths for development and differentiation. Proceedings of the National Academy of Sciences, 108(20), 8257-8262. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1073/pnas.1017017108")}

See Also

sim_fun_grad() and batch_simulation().

simlandr documentation built on April 4, 2025, 1:14 a.m.