Table 5.
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/μ − νδ) > 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/(μ − νδ), 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) − λmα2βP(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) |