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
[0] saddle 2, displaced by +1e-05 x unstable eigenvector (eigenvalue 2.9094e-08) S(0) = 0.976986484 -> S(T) = 0.980131721303: steady state 3 (largest difference of a coordinate 4.0e-11; |right-hand side| 1.3e-17); feasible all the time: True; 1775 steps, 43 s
      t=1e+02: S=0.976986484; t=1e+05: S=0.976986511; t=1e+07: S=0.976990068; t=1e+08: S=0.977183563; t=3e+08: S=0.980000542; t=1e+09: S=0.980131721; t=3e+09: S=0.980131721; t=6e+09: S=0.980131721
[1] saddle 2, displaced by -1e-05 x unstable eigenvector (eigenvalue 2.9094e-08) S(0) = 0.976966484 -> S(T) = 0.973078759109: steady state 1 (largest difference of a coordinate 9.4e-11; |right-hand side| 2.2e-17); feasible all the time: True; 1775 steps, 44 s
      t=1e+02: S=0.976966484; t=1e+05: S=0.976966451; t=1e+07: S=0.976962876; t=1e+08: S=0.976753283; t=3e+08: S=0.973079671; t=1e+09: S=0.973078759; t=3e+09: S=0.973078759; t=6e+09: S=0.973078759
[2] saddle 4, displaced by +1e-05 x unstable eigenvector (eigenvalue 2.7739e-08) S(0) = 0.982443429 -> S(T) = 0.983715309126: steady state 5 (largest difference of a coordinate 2.2e-11; |right-hand side| 4.5e-18); feasible all the time: True; 1775 steps, 38 s
      t=1e+02: S=0.982443429; t=1e+05: S=0.982443449; t=1e+07: S=0.982446822; t=1e+08: S=0.982619891; t=3e+08: S=0.983715168; t=1e+09: S=0.983715309; t=3e+09: S=0.983715309; t=6e+09: S=0.983715309
[3] saddle 4, displaced by -1e-05 x unstable eigenvector (eigenvalue 2.7739e-08) S(0) = 0.982423429 -> S(T) = 0.980131721586: steady state 3 (largest difference of a coordinate 2.4e-10; |right-hand side| 2.6e-18); feasible all the time: True; 1775 steps, 29 s
      t=1e+02: S=0.982423429; t=1e+05: S=0.982423391; t=1e+07: S=0.982420019; t=1e+08: S=0.982252050; t=3e+08: S=0.980226215; t=1e+09: S=0.980131721; t=3e+09: S=0.980131721; t=6e+09: S=0.980131722
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
