Skip to main content
. 2018 Dec 4;2018:7930603. doi: 10.1155/2018/7930603

Table 5.

The values calculated from Table 4 according to Table 2.

Expressions Terms Values
For Figure 2 For Figure 3 For Figure 4
Equilibrium point E1 E 1(Λ, 0) E 1(1,0) E 1(10,0) E 1(5,0)
Stability condition of E1 (δ/μνδ) > Λ 10 > 1 (E1 is LAS) 0.50 < 10 (E1 is unstable) 0.50 < 5 (E1 is unstable)
Equilibrium point E2 E 2(P=δ/(μνδ), T=βP(1 − (P/Λ))/(c/(1+aP))) E 2(10, −16.20)(biologically meaningless) E 2(0.50, 1.71) E 2(0.50, 0.81)
Parameter A1 (1 − (P/Λ)) 0.95 0.90
Parameter A2 (aP/aP+1) 0.66667 0.3333
Least common multiple of order's denominator m 5 5
Characteristical equation of eigenvalues for E2 λ m(α1+α2)λ2βP(A1(A2+1) − 1)+((βPδ2A1)/(μΛ(1 − A1)))=0 λ 7 − 1.40λ3+1.1692=0 λ 7 − 0.48λ3+1.1077=0
The eigenvalues for E2 λ 1 ≈ 0.9614+0.2454i
λ2 ≈ 0.9614 − 0.2454i
λ3 ≈ 0.1199+1.1495i
λ4 ≈ 0.1199 − 1.1495i
λ5 ≈ −1.2004
λ6 ≈ −0.4812+0.7135i
λ7 ≈ −0.4812 − 0.7135i
λ 1 ≈ 0.9287+0.3757i
λ2 ≈ 0.9287 − 0.3757i
λ3 ≈ 0.1852+1.0410i
λ4 ≈ 0.1852 − 1.0410i
λ5 ≈ −1.0798
λ6 ≈ −0.5741+0.7646i
λ7 ≈ −0.5741 − 0.7646i
Angle of eigenvalues for E2 θ=arg(λ) θ 1 ≈ 14.3191°,
θ2 ≈ −14.3191°,
θ3 ≈ 84.0452°,
θ4 ≈ −84.0452°,
θ5 ≈ 180°,
θ6 ≈ 123.997°,
θ7 ≈ −123.997°
θ 1 ≈ 22.0255°,
θ2 ≈ −22.0255°,
θ3 ≈ 79.9123°,
θ4 ≈ −79.9123°,
θ5 ≈ 180°,
θ6 ≈ 126.901°,
θ7 ≈ −126.901°
Stability condition of E2 |θi| > (π/2m) E 2 is an unstable point, since |θ1|, |θ2| ≈ 14.31° < 18°. E 2 is LAS, since |θ1|, |θ2|,…, |θ7| > 18°.
Initial conditions (P0, T0) (0.3, 0.01) (0.3, 0.01) (0.3, 0.01)