Table 2 Stability analysis of equilibrium points
E | Jacobian matrix eigenvalues | S | C | |||
|---|---|---|---|---|---|---|
\(\lambda_{1}\) | \(\lambda_{2}\) | \(\lambda_{3}\) | RPS | |||
E1(0,0,0) | \(Q_{1} - C_{1} - Q_{2} + C_{2}\) | \(H - C_{g} + P\) | \((W_{1} - S_{1} )(1 - n) - (W_{2} - S_{2} ) - L\) | (U, + , U) | N | / |
E2(1,0,0) | \(Q_{1} - C_{1} - Q_{2} + C_{2}\) | \(C_{g} - H - P\) | \(H + T - (W_{2} - S_{2} ) + (W_{1} - S_{1} )(1 - n)\) | (U, -, U) | ESS | a |
E3(0,1,0) | \(Q_{1} - C_{1} - Q_{3} + C_{3}\) | \(L + (W_{2} - S_{2} ) - (W_{1} - S_{1} )(1 - n)\) | \(- C_{g} - L - T - U\) | (U, U, -) | ESS | b |
E4(0,0,1) | 0 | \(P - C_{g}\) | \(Q_{2} - C_{2} - Q_{1} + C_{1}\) | (0, + , U) | N | / |
E5(1,1,0) | \(Q_{1} - C_{1} - Q_{3} + C_{3}\) | \((W_{2} - S_{2} ) - T - H - (W_{1} - S_{1} )(1 - n)\) | \(C_{g} + L + T + U\) | (U, U, +) | N | / |
E6(1,0,1) | \(T\) | \(C_{g} - P\) | \(Q_{2} - C_{2} - Q_{1} + C_{1}\) | (+ , -, U) | N | / |
E7(0,1,1) | 0 | \(Q_{3} - C_{3} - Q_{1} + C_{1}\) | \(D - C_{g} - T\) | (0, U, U) | N | / |
E8(1,1,1) | \(Q_{3} - C_{3} - Q_{1} + C_{1}\) | \(- T\) | \(- D + C_{g} + T\) | (U, -, U) | ESS | c |