Table 3. Stability analysis of equilibrium points.
| Equilibrium points | Eigenvalues | Symbols | State | Conditions | ||
|---|---|---|---|---|---|---|
| λ 1 | λ 2 | λ 3 | ||||
| E1(0,0,0) | R1-C2-Cr-C1+R2 | R4-C3 | Rg-Cg | (+,+,+) | Instability point | \ |
| E2(1,0,0) | C1+C2+Cr-R1-R2 | R4-C3+C1*ω1+C2*ω2-R1*ω1-R2*ω2 | Rg-Cg-S1 | (-,+,+) | Instability point | ① |
| E3(0,1,0) | R1-C2-Cr-C1+R2 | C3-R4 | Rg-Cg-S2 | (+,-,+) | Instability point | \ |
| E4(0,0,1) | R1-C2-Cr-C1+R2+S1 | R4-C3+S2 | Cg-Rg | (+,+,-) | Instability point | \ |
| E5(1,1,0) | C1+C2+Cr-R1-R2 | C3-R4-C1*ω1-C2*ω2+R1*ω1+R2*ω2 | Rg-Cg-S1-S2 | (-,-,+) | Instability point | ① |
| E6(1,0,1) | C1+C2+Cr-R1-R2-S1 | R4-C3+S2+C1*ω1+C2*ω2-R1*ω1-R2*ω2 | Cg-Rg+S1 | (-,+,-) | Instability point | ① |
| E7(0,1,1) | R1-C2-Cr-C1+R2+S1 | C3-R4-S2 | Cg-Rg+S2 | (+,-,-) | Instability point | \ |
| E8(1,1,1) | C1+C2+Cr-R1-R2-S1 | C3-R4-S2-C1*ω1-C2*ω2+R1*ω1+R2*ω2 | Cg-Rg+S1+S2 | (-,-,-) | ESS② | ① |
①:R4-C3>|C1*ω1+C2*ω2-R1*ω1-R2*ω2|.
②:ESS is the evolutionary stable strategy of the system.