TABLE 1.

Existence and stability of S1, S2 and S3. The feedbacks are Hill functions with exponent one.

	S1	S2	S3
p̄0 ≤ 0.5,p̄1 ≤ 0.5	Globally stable	Does not exist	Does not exist
p̄0 ≤ 0.5,p̄1 > 0.5	Locally unstable If χ(0) = (0, 0, χ2), then χ(t) → (0, 0, 0) as t → ∞	Locally stable If χ(0) = (χ0, χ1, χ2) when χ0 ≠ 0 or χ1 ≠ 0, then $\chi (t)\to (0,{\chi }_1^{**},{\chi }_2^{**})$ as t → ∞	Does not exist
p̄0 > 0.5,p̄1 ≤ 0.5	Locally unstable If χ(0) = (0, 0, χ2), then χ(t) → (0, 0, 0) as t → ∞	Does not exist	Exists Stability – Section 4.3
p̄0 > 0.5,p̄1 > 0.5 if (36) is not true	Locally unstable If χ(0) = (0, 0, χ2), then χ(t) → (0, 0, 0) as t → ∞	Locally stable If χ(0) = (0, χ1, χ2) when χ1 ≠ 0, then $\chi (t)\to (0,{\chi }_1^{**},{\chi }_2^{**})$ as t → ∞	Does not exist
p̄0 > 0.5,p̄1 > 0.5 if (36) is true	Locally unstable If χ(0) = (0, 0, χ2), then χ(t) → (0, 0, 0) as t → ∞	Locally unstable If χ(0) = (0, χ1, χ2) when χ1 ≠ 0, then $\chi (t)\to (0,{\chi }_1^{**},{\chi }_2^{**})$ as t → ∞	Exists Stability – Section 4.3