r2_dynamics.py (verification run 2); numpy 2.5.4; N = 1000; floating point, NOT a proof
steady states (S): 0.973078759015, 0.976976484125, 0.980131721344, 0.982433429148, 0.983715309104
largest |right-hand side| at the five rounded states: 3.5e-18, 1.7e-18, 1.7e-18, 8.7e-19, 8.7e-19
[8] generic start S(0) = 0.9813, all C_j(0) = 0.5/(N+1) S(0) = 0.981300000 -> S(T) = 0.983715309102: steady state 5 (largest difference of a coordinate 2.2e-12; |right-hand side| 5.1e-18); feasible all the time: True; 1775 steps, 31 s
      t=1e+02: S=0.981581993; t=1e+05: S=0.987011255; t=1e+07: S=0.984098014; t=1e+08: S=0.983716241; t=3e+08: S=0.983715309; t=1e+09: S=0.983715309; t=3e+09: S=0.983715309; t=6e+09: S=0.983715309
[9] generic start S(0) = 0.9831, all C_j(0) = 0.5/(N+1) S(0) = 0.983100000 -> S(T) = 0.983715309127: steady state 5 (largest difference of a coordinate 2.2e-11; |right-hand side| 1.7e-18); feasible all the time: True; 1775 steps, 34 s
      t=1e+02: S=0.983299492; t=1e+05: S=0.987071413; t=1e+07: S=0.984098945; t=1e+08: S=0.983716242; t=3e+08: S=0.983715309; t=1e+09: S=0.983715309; t=3e+09: S=0.983715309; t=6e+09: S=0.983715309
[10] generic start S(0) = 0.99, all C_j(0) = 0.9/(N+1) S(0) = 0.990000000 -> S(T) = 0.973078759063: steady state 1 (largest difference of a coordinate 4.8e-11; |right-hand side| 1.7e-18); feasible all the time: True; 1775 steps, 41 s
      t=1e+02: S=0.989894152; t=1e+05: S=0.981641891; t=1e+07: S=0.970814867; t=1e+08: S=0.973075558; t=3e+08: S=0.973078759; t=1e+09: S=0.973078759; t=3e+09: S=0.973078759; t=6e+09: S=0.973078759
[11] generic start S(0) = 0.2, all C_j(0) = 0.9/(N+1) S(0) = 0.200000000 -> S(T) = 0.973078759088: steady state 1 (largest difference of a coordinate 7.3e-11; |right-hand side| 4.0e-18); feasible all the time: True; 1775 steps, 43 s
      t=1e+02: S=0.202012338; t=1e+05: S=0.204551187; t=1e+07: S=0.970204614; t=1e+08: S=0.973075129; t=3e+08: S=0.973078759; t=1e+09: S=0.973078759; t=3e+09: S=0.973078759; t=6e+09: S=0.973078759
all trajectories of this call stay feasible and converge to one of the steady states 1, 3, 5; the saddle starts reach the two neighbours: True
