Algorithm 4 A sufficient topological criterion for P.

Search for cycles with period $T\le T_{max}$;⁡ Evaluate the multiplier ΛT; Check for return   $d_n^{\left(T\right)}=|{\mathrm{z}}_{\mathrm{n}+\mathrm{T}}-{\mathrm{z}}_{\mathrm{n}}|$; Take the sequence of vertices ${{\{z}_n\}}_{n-0}^{N-1}$ (after the transition); Fix Tmax, ԑ and a majority threshold θ; For each $T=1,\dots ,T_{max}$ calculate the returns          $d_n^{\left(T\right)}=\left|z_{n+T}-z_n\right|$ for n = 0,…, N − T − 1, we write the division             $∆r_T={\displaystyle \frac{1}{N-T}}\#\{n:d_n^{\left(T\right)}<\mathrm{ԑ}\};$ 7.If there is no T with $r_T$ ≥ θ, there is no observable periodicity for T ≤ Tmax; 8.For each T with small $d_n^{\left(T\right)}$ evaluate locally P′(z) by linear fit of the points (zn, zn+1) in a small circle around each of the T nodes of the cycle candidate; multiply the derivatives along the path → ${\Lambda }_{\mathrm{T}}\left(z\right)=\prod _{j-0}^{T-1}{P}^{\prime }\left(z_j\right);$ 9.If for all found candidates |ΛT| ≥ 1 classify the regime as non-periodic unstable; 10.If for some T there is $r_T$ ≥ θ and |ΛT| < 1, reclassify as non-periodic stable.