Compares random matrices in which variation in component response rate does not vary to random matrices in which this variation for 2 to max_sp components. This function is to be used for random networks, in which off-diagonal elements are randomly sampled from a normal distribution with a mean of 'mn' and a standard deviation of 'sigma'.
rand_gen_var(max_sp, iters, int_type = 0, rmx = 0.4, C = 1, by = 1, sigma = 0.4, mn = 0, dval = 1, g_dist = 1, g_mn = 1, g_sd = 1)
| max_sp | Maximum number of components to randomise |
|---|---|
| iters | Number of iterations (i.e., random matrices) per component |
| int_type | Type of interaction between components including random (0), competitor (1), mutualist (2), predator-prey (3), and cascade model (4) |
| rmx | Standard deviation of population growth rates (for feasibility) |
| C | Connectedness of matrices (i.e., probability of non-zero matrix element components. |
| by | Sequence between component number to randomise (e.g., '2': 2, 4, 6) |
| sigma | Standard deviation of interaction strength among network elements |
| mn | Mean interaction strength among network elements |
| dval | Self-regulation of network elements (1 by default) |
| g_dist | Gamma distribution to be used (1 by default) |
| g_mn | Mean value of gamma distribution (only for g_dist 0) |
| g_sd | Standard deviation of gamma distribution (only for g_dist 2-4) |
A table of stability results, where rows summarise for each component number (S) the number of stable or unstable (also, feasible and infeasible) random matrices produced.
rand_gen_var(max_sp = 2, iters = 4);#> [1] 2#> S A_unstable A_stable M_unstable M_stable A_stabilised A_destabilised #> [1,] 2 0 4 0 4 0 0 #> A_infeasible A_feasible M_infeasible M_feasible A_made_feasible #> [1,] 2 2 2 2 0 #> A_made_infeasible A_rho M_rho rho_diff rho_abs complex_A complex_M #> [1,] 0 NA NA NA NA 0.490642 0.4704908 #> A_eig M_eig LR_A UR_A LR_M UR_M #> [1,] -0.9688859 -0.914339 -1.03744 -0.8022137 -1.023615 -0.8007735