Multiagent Game of Intelligent Building Detection and Its Harm Rumor Analysis

Table 2

Stability analysis of equilibrium point.

Stable point	Eigenvalue of Jacobian matrix				Stability conclusion	Condition
	λ1	λ2	λ3	Real part
E1 (0, 0, 0)	−Bt + Ct + Mt	Csl − Csh + Cs + Bt	Fs +  + Ft  −	(−, −, +)	Unstable point	—
E2 (1, 0, 0)	Ct	Ft −  − Ms	Csh − Csl − Cs − Bt	(+, +, )	Unstable point	—
E3 (0, 1, 0)	Csl−Csh + Cs + Rs	Bt − Ct − Mt	Fs − Mt −	(+, +, )	Unstable point	—
E4 (0, 0, 1)	Csl − Csh + Cs + Bt + Fs + Ms	Mt + Ft + Ct − Bt	−Fs −  − Ft +	(−, −, −)	ESS	①
E5 (1, 1, 0)	−Csl + Csh − Cs − Rs	−Ct	−Ms − Mt −	(−, −, −)	ESS	—
E6 (1, 0, 1)	−Csl + Csh − Cs − Bt − Fs − Ms	Mt + Ft + Ct	Ms − Ft +	(, +, )	Unstable point	—
E7 (0, 1, 1)	Csl − Csh + Cs + Bt + Fs + Ms	Bt − Ct − 2Mt − Ft	Mt − Fs +	(+, , )	Unstable point	—
E8 (1, 1, 1)	Ms + Mt +	−Mt − Ft − Ct	−Csl + Csh − Cs − Rs − Fs − Ms	(−, −, +)	Unstable point	—
E9 (0, y1, z1)				(−, 0, 0)	Cannot be determined	②
E10 (x1, 0, z2)				(−, 0, 0)	Cannot be determined	③
E12 (x2, y2, 0)				(, +, −)	Unstable point	④
E13 (x3, y3, 1)				(, +, −)	Unstable point	⑤

Notes: ω indicates the expression is too long, indicates that the symbol is uncertain, and x₁, x₂, x₃, y₁, y₂, y₃, z₁, z₂, respectively, indicate the coordinates of the corresponding balance point. If they do not meet the requirements, the balance point is meaningless or unstable. ① C_sl − C_sh + C_s + B_t + F_st + M_s < 0, M_t + F_t + C_t − B_t < 0; ② a₁ < 0, F_s − < M_t, B_t − C_t − F_t − M_t < 0; ③ a₂ < 0, F_t − < M_s, C_sh − C_sl −C_s − B_t − F_s − M_s < 0, − < M_s, C_sh − C_sl − C_s − B_t − F_s − M_s < 0; ④ B_t − C_t > 0, C_sh − C_sl − C_s − B_t > 0; ⑤ B_t − M_t − F_t − C_t > 0, C_sh − C_sl − C_s − B_t > 0.