Heteroclinic Cycles of a Symmetric May-Leonard Competition Model with Seasonal Succession

The paper proves existence of a 2D carrying simplex Σ and a boundary heteroclinic cycle Γ under (H̃), computes invasion multipliers e^{h_j−a_{ji}h_i}, and establishes the stability criterion via ϑ=∏(h_i−βh_{i−1})+∏(h_i−αh_{i+1}) with Γ repelling if ϑ>0 and attracting if ϑ<0; it also treats the symmetric case λ1=λ2=λ3, deriving the α+β threshold and the flat simplex at α+β=2. The candidate solution follows the same carrying‑simplex and boundary‑index route, derives the same multipliers and criterion, and reproduces the symmetric-case conclusions. The only issue is a minor algebraic slip in an intermediate axis map formula (a missing factor e^{-p_i} in the denominator), which the candidate’s subsequent fixed‑point expression corrects. Overall, methods and results agree with the paper.