Compares small world networks 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 small world networks, which are constructed using the method of Watts and Strogatz (Nature vol. 393, 1998). Off-diagonal elements have a mean of 'mn' and a standard deviation of 'sigma'.
rand_gen_swn(max_sp, iters, int_type = 0, rmx = 0.4, C = 1, by = 4, sigma = 0.4, Kdiv = 2, beta = 0.2, 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 |
| Kdiv | Value to divide the component number by to produce the parameter K for creating the small world network. For example, if S = 32 and K = 8, then the small world network will be created from a regular network in which each component is connected to 32/8 = 4 other components. This needs to be used cautiously to avoid generating non-even values of K. |
| beta | Probability that a random interaction in a regular network is rewired (parameter p in Watts and Strogatz 1998) |
| mn | Mean interaction strength among network elements |
| dval | Self-regulation of network elements (1 by default) |
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_swn(max_sp = 16, iters = 4);#> [1] 4 #> [1] 8 #> [1] 12 #> [1] 16#> S A_unstable A_stable M_unstable M_stable A_stabilised A_destabilised #> [1,] 4 0 4 0 4 0 0 #> [2,] 8 0 4 0 4 0 0 #> [3,] 12 1 3 1 3 0 0 #> [4,] 16 2 2 2 2 0 0 #> A_infeasible A_feasible M_infeasible M_feasible A_made_feasible #> [1,] 3 1 2 2 1 #> [2,] 4 0 4 0 0 #> [3,] 4 0 4 0 0 #> [4,] 4 0 4 0 0 #> A_made_infeasible A_rho M_rho rho_diff rho_abs #> [1,] 0 0.48002817 0.47099459 -0.009033579 -0.093580519 #> [2,] 0 -0.20671475 -0.08362409 0.123090655 -0.111340582 #> [3,] 0 0.01890760 -0.05110404 -0.070011641 0.007472452 #> [4,] 0 -0.05063846 -0.01701563 0.033622827 0.012830877 #> complex_A complex_M A_eig M_eig LR_A UR_A #> [1,] 0.2604540 0.2967713 -0.6099816 -0.18354042 -0.7520473 -0.27942635 #> [2,] 0.9894985 1.0599191 -0.6602999 -0.23753169 -0.9933007 -0.36713952 #> [3,] 1.0471728 1.1901489 -0.1494897 -0.10419012 -0.5212001 0.01127894 #> [4,] 1.1475764 1.2813031 -0.1131102 -0.04551905 -0.3586204 0.14837376 #> LR_M UR_M C #> [1,] -0.4752191 -0.027533847 0.9166667 #> [2,] -0.4184222 -0.033937879 0.6696429 #> [3,] -0.3801035 0.002562937 0.5795455 #> [4,] -0.1967054 0.150238150 0.5666667