Let their numbers at time t be y(t) and x(t) respectively, and it is best to provide data. It is assumed that there is 100 each.

Using matlab to solve the numerical problem;

Functional rabbit

[t，X]=ode45(@fun，[0 10]，[ 100 100])

Drawing (t, x)

Function d=fun(t, x)

X = X( 1)； y = X(2)；

dy = 0.00 1 * x * y-0.9 * y；

dx = 4 * x-0.02 * x * y；

d =[dx； dy]；

Get the result: (you can use excel to draw)

t =

0.025 1

0.0502

0.0754

0. 1005

0.2073

0.3 142

0.42 10

0.5278

0.6442

0.7606

0.8769

0.9933

1.0863

1. 1792

1.2722

1.3652

1.4582

1.55 12

1.644 1

1.737 1

1.7720

1.8069

1.84 18

1.8767

1.9 1 16

1.9465

1.98 13

2.0 162

2.0640

2. 1 1 17

2. 1594

2.2072

2.2547

2.3022

2.3497

2.3972

2.4439

2.4906

2.5373

2.5840

2.6480

2.7 120

2.7760

2.8400

2.9225

3.0050

3.0875

3. 1700

3.26 15

3.353 1

3.4446

3.536 1

3.6735

3.8 1 10

3.9484

4.0858

4.259 1

4.4324

4.6058

4.779 1

4.92 10

5.0629

5.2048

5.3468

5.4280

5.5092

5.5905

5.67 17

5.7096

5.7474

5.7853

5.8232

5.86 10

5.8989

5.9368

5.9746

6.0276

6.0805

6. 1334

6. 1863

6.2383

6.2903

6.3423

6.3943

6.437 1

6.4800

6.5228

6.5657

6.6200

6.6744

6.7288

6.783 1

6.8650

6.9468

7.0286

7. 1 104

7. 1922

7.274 1

7.3559

7.4377

7.5505

7.6634

7.7763

7.889 1

8.0776

8.2660

8.4544

8.6429

8.8032

8.9636

9. 1239

9.2843

9.37 17

9.4590

9.5464

9.6338

9.6689

9.7040

9.7392

9.7743

9.8094

9.8445

9.8797

9.9 148

9.936 1

9.9574

9.9787

10.0000

X =

1.0e+003 *

0. 1000 0. 1000

0. 1052 0.0980

0. 1 108 0.096 1

0. 1 168 0.0942

0. 1232 0.0924

0. 1563 0.0852

0.20 12 0.0788

0.262 1 0.0734

0.3453 0.0688

0.4706 0.0650

0.6465 0.0624

0.8922 0.06 14

1.2309 0.0625

1.5836 0.0656

2.0252 0.07 13

2.5545 0.0809

3. 1433 0.0970

3.74 12 0. 1222

4. 1562 0. 1633

4. 195 1 0.2235

3.7563 0.2986

3.470 1 0.3283

3. 14 1 1 0.357 1

2.7886 0.3838

2.432 1 0.4074

2.0896 0.4272

1.7732 0.4428

1.4904 0.4542

1.2447 0.46 16

0.9675 0.4660

0.750 1 0.465 1

0.5825 0.4599

0.4555 0.45 15

0.3604 0.44 1 1

0.288 1 0.429 1

0.2328 0.4 163

0. 1905 0.4029

0. 1586 0.3894

0. 1337 0.3760

0. 1 142 0.3626

0.0987 0.3494

0.0824 0.33 17

0.0704 0.3 147

0.06 14 0.2983

0.0547 0.2827

0.0485 0.2636

0.0443 0.2456

0.04 17 0.2289

0.0403 0.2 132

0.0399 0. 197 1

0.0407 0. 1822

0.0426 0. 1684

0.0456 0. 1557

0.0528 0. 1385

0.0639 0. 1234

0.0803 0. 1 10 1

0. 1045 0.0985

0. 1523 0.0862

0.2294 0.076 1

0.3569 0.0685

0.5693 0.0634

0.8367 0.06 18

1.242 1 0.0629

1.8286 0.0684

2.608 1 0.0822

3. 1250 0.0964

3.6366 0. 1 180

4.0532 0. 1502

4.2464 0. 1958

4.2 186 0.2222

4. 1034 0.25 14

3.9004 0.2828

3.6 188 0.3 152

3.2760 0.3472

2.8970 0.3772

2.507 1 0.4038

2. 1293 0.426 1

1.6555 0.4488

1.2620 0.462 1

0.9526 0.467 1

0.7 188 0.4654

0.5473 0.4589

0.4 197 0.449 1

0.3244 0.4369

0.2542 0.4232

0.2 1 10 0.4 1 13

0. 1770 0.3990

0. 1500 0.3866

0. 1285 0.3742

0. 1072 0.3586

0.09 10 0.3433

0.0785 0.3285

0.0688 0.3 140

0.0580 0.2932

0.0507 0.2736

0.0456 0.2552

0.0422 0.2379

0.0402 0.22 18

0.0393 0.2067

0.0393 0. 1927

0.0402 0. 1796

0.0430 0. 1630

0.0475 0. 1480

0.0543 0. 1345

0.0638 0. 1223

0.0888 0. 1047

0. 1303 0.0902

0.20 14 0.0785

0.3250 0.0695

0.496 1 0.0643

0.7720 0.06 15

1.2078 0.0620

1.8628 0.0685

2.3274 0.076 1

2.8637 0.0882

3.43 13 0. 1073

3.939 1 0. 1368

4.0958 0. 1527

4.2073 0. 17 12

4.26 19 0. 1925

4.2490 0.2 166

4. 16 10 0.2433

3.996 1 0.272 1

3.759 1 0.3022

3.46 17 0.3324

3.2593 0.3503

3.0458 0.3675

2.8260 0.3838

2.6046 0.3990