Evolutionary Game and Simulation of Green Housing Market Subject Behavior in China

Table 2

Eigenvalues of the Jacobian matrix and local stability judgment of equilibrium point.

Equant equation	Eigenvalues of the Jacobian matrix		Stability conclusion	Condition
	λ1, λ2, λ3	Real component symbol
E1[0, 0, 0]	AQ − AP − CZ, φSZ1 + ηSZ2 − AZ, G1 − D1	(×, −, ×)	Stable point	①
E2[0, 0, 1]	θD2 + AQ − AP − CZ, (1 − θ)D2 + φSZ1 + ηSZ2 − AZ, D1 − G1	(×, +, ×)	Instable point	—
E3[1, 0, 0]	CZ + AP − AQ, φSZ1 + ηSZ2 − AZ, G1 − D1 − θD2	(×, −, ×)	Stable point	②
E4[0, 1, 0]	AQ + AP + AZ − CZ, AZ − φSZ1 − ηSZ2, G1 − D1 − (1 − θ)D2	(+, +, −)	Instable point	—
E5[1, 1, 0]	CZ − AP − AZ − AQ, AZ − φSZ1 − ηSZ2, G1 − D1 − D2	(−, −, +)	Instable point	—
E6[0, 1, 1]	θD2+AQ + AP + AZ − CZ, AZ − φSZ1 − ηSZ2 − (1 − θ)D2, (1 − θ)D2 + D1 − G1	(+, −, −)	Instable point	—
E7[1, 0, 1]	CZ + AP − θD2 − AQ, (1 − θ)D1 + φSZ1 + ηSZ2 − AZ, θD2+D1 − G1	(+, +, −)	Instable point	—
E8[1, 1, 1]	CZ − AZ − AP − θD2 − AQ, AZ − φSZ1 − ηSZ2 − (1 − θ)D2, D2 + D1 − G1	(−, −, ×)	Stable point	③

Note. x means the symbol is uncertain, ① A_Q − A_P − C_Z < 0, G₁ − D₁ < 0; ② C_Z + A_P − A_Q < 0, G₁ − D₁ − θD₂ < 0; ③ D₂ + D₁ − G₁ < 0.