Compares scale-free networks in which variation in component response rate does not vary to random matrices in which this variation for 'm' to 'max_sp' components. This function is to be used for scale-free networks, which are constructed using the method of Albert and Barab\'asi (Reviews of Modern Physics, Vo. 74, 2002). Off-diagonal elements have a mean of 'mn' and a standard deviation of 'sigma'.
rand_gen_sfn(S, m_vals, iters, int_type = 0, rmx = 0.4, sigma = 0.4, mn = 0, dval = 1, g_dist = 1, g_mn = 1, g_sd = 1)
| S | Number of components to randomise |
|---|---|
| m_vals | The number of vertices that newly added components will have in the scale free network (increasing this, but not S, increases the complexity by increasing C). |
| 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) |
| 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) |
| C | Connectedness of matrices (i.e., probability of non-zero matrix element components. |
| m | The number of vertices that newly added components will have in scale-free network construction |
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.
#> [1] 2 #> [1] 4#> S A_unstable A_stable M_unstable M_stable A_stabilised A_destabilised #> [1,] 2 0 4 0 4 0 0 #> [2,] 4 2 2 2 2 0 0 #> A_infeasible A_feasible M_infeasible M_feasible A_made_feasible #> [1,] 4 0 4 0 0 #> [2,] 4 0 4 0 0 #> A_made_infeasible A_rho M_rho rho_diff rho_abs #> [1,] 0 -0.04580611 -0.02512778 0.02067833 -0.01217005 #> [2,] 0 -0.06617231 -0.09111299 -0.02494068 0.06270303 #> complex_A complex_M A_eig M_eig LR_A UR_A #> [1,] 0.8904277 0.9753995 -0.44171862 -0.09445092 -0.6084554 -0.2584511 #> [2,] 1.1186440 1.3316457 0.03644578 0.10779208 -0.1298998 0.3617342 #> LR_M UR_M C #> [1,] -0.22631126 -0.01915051 0.1648551 #> [2,] -0.02932164 0.46835811 0.3134058