Table 1 FBQP model.(2) in Case I, where \(A,B,x_{-2},x_{-1},x_{0}\) are fuzzy parameters in (4.2)

From: Dynamic analysis of a fuzzy Bobwhite quail population model under g-division law

 

\(A_{r}\)

\(B_{r}\)

\(x_{-2,r}\)

\(x_{-1,r}\)

\(x_{0,r}\)

\(x_r\)

\(x^*_{r}\)

\(A_{l}\)

\(B_{l}\)

\(x_{-2,l}\)

\(x_{-1,l}\)

\(x_{0,l}\)

\(x_l\)

\(x^*_{l}\)

\(\alpha \)=0

2.0000

0.3500

1.2500

1.3500

1.4500

(2.0000,6.4500)

3.5147

 

1.5000

0.1500

0.7500

0.6500

0.5500

(1.5000,4.4486)

2.2806

\(\alpha \)=0.25

1.9665

0.3366

1.2165

1.3031

1.3897

(1.9665,6.2476)

3.4068

 

1.5335

0.1634

0.7835

0.6969

0.6103

(1.5335,4.5114)

2.3431

\(\alpha \)=0.5

1.9268

0.3207

1.1768

1.2475

1.3182

(1.9268,6.0185)

3.2846

 

1.5732

0.1793

0.8232

0.7525

0.6818

(1.5732,4.5989)

2.4203

\(\alpha \)=0.75

1.8750

0.3000

1.1250

1.1750

1.2250

(1.8750,5.7370)

3.1344

 

1.6250

0.2000

0.8750

.82500

0.7750

(1.6520,4.7321)

2.5261

\(\alpha \)=1

1.7500

0.2500

1.0000

1.0000

1.0000

(1.7500,5.1325)

2.8081

 

1.7500

0.2500

1.0000

1.0000

1.0000

(1.7500,5.1325)

2.8081

  1. The fuzzy positive solution is proved to be bounded and persistent that \(x_n \in (x_{l,\alpha },x_{r,\alpha })=(A_{l,\alpha },\frac{A_{r,\alpha }^3}{(1-B_{r,\alpha })A_{l,\alpha }^2-1}+x_{3,r,\alpha })\), and its fuzzy equilibrium solution is \((x^*_{l,\alpha },x^*_{r,\alpha })\) as the following table shows.
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