Figure 1

Relation of fixed points and parameters for the system in all regimes. The regime represented by III i) with parameters regions σ ∊ (σ₁, σ₂) and $\mu \in (2/\left(2N-1+2\sqrt{N\left(N-1\right))},1\right)$ has two imaginary fixed points. The red curve denoted by II) with parameters satisfying σ = σ ₂ and $\mu \in (2/(2N-1+2\sqrt{N\left(N-1\right))},1)$ has two equivalent fixed points. The three cases of II) occur in the intervals. The regimes denoted by I) with parameters satisfying σ ∊ (σ₂,σ₅) and $\mu \in (2/\left(2N-1+2\sqrt{N\left(N-1\right))},\left(2N-1\right)/4N\left(N-1\right)\right)$; satisfying σ ∊ (σ₂, σ₅) and μ ∊ ((2N - 1)/4N(N - 1), 1); satisfying σ ∊ (σ ₁,σ₅) and μ ∊ (0,1/(2N - 1)); satisfying σ ∊ (σ ₁,σ ₅ ) and $\mu \in (1/\left(2N-1\right),2/(2N-1+2\sqrt{N\left(N-1\right))})$ have two real fixed points. The five cases of I) occur in the regions.