sim_fun_nongrad {simlandr} | R Documentation |
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. |
constrain_a |
Should the value of |
amin , amax |
If |
length |
The length of simulation. |
stepsize |
The step size used in the Euler method. |
seed |
The initial seed that will be passed to |
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. doi:10.1073/pnas.1017017108
See Also
sim_fun_grad()
and batch_simulation()
.