Theory and Modern Applications

# Table 1 Parameters in the system of difference equations ( 1 )-( 7 )

Parameter

Definition

$$\boldsymbol{t=25^{\circ}}\mathbf{C}$$

$$\boldsymbol{t=27^{\circ}}\mathbf{C}$$

$$\boldsymbol{t=30^{\circ}}\mathbf{C}$$

• Mealybugs

$$\alpha_{1}$$

The fraction of mealybug’s eggs that develop into instar mealybugs in one time step

0.1075

0.1163

0.1493

$$\alpha_{2}$$

The fraction of instar mealybugs that develop into adult mealybugs in one time step

0.0435

0.0482

0.0388

$$\alpha_{3}$$

The natural death rate of adult mealybugs

0.0612

0.0665

0.0596

$$\alpha_{4}$$

The fraction of female adult mealybugs in the reproductive period

0.4591

0.4991

0.4468

$$r_{1}$$

The survival rate of mealybug’s eggs that develop into instar mealybugs

0.8900

0.8700

0.9120

$$r_{2}$$

The survival rate of instar mealybugs that develop into adult mealybugs

0.7737

0.6079

0.6589

$$r_{3}$$

The fraction of female adult mealybugs

0.7400

0.7200

0.8500

$$v_{1}$$

The average number of eggs laid by a female adult mealybug in one time step

40.0000

36.5300

2.9126

• Green lacewings

$$\gamma_{1}$$

The fraction of green lacewing’s eggs that develop into larva green lacewing in one time step

0.1639

0.2222

0.2703

$$\gamma_{2}$$

The fraction of larva green lacewings that develop into pupa green lacewing in one time step

0.0521

0.0585

0.00625

$$\gamma_{3}$$

The fraction of pupa green lacewings that develop into adult green lacewings in one time step

0.0714

0.0885

0.1053

$$\delta_{2}$$

The natural death rate of adult green lacewings

0.0227

0.0175

0.0206

$$s_{1}$$

The survival rate of green lacewing’s eggs that develop into larva green lacewing

0.8040

0.8210

0.8170

$$s_{2}$$

The survival rate of larva green lacewing that develop into pupa green lacewing

0.9191

0.9629

0.7938

$$s_{3}$$

The survival rate of pupa green lacewing that develop into adult green lacewings

0.9586

0.9614

0.7402

$$s_{4}$$

The fraction of female adult green lacewings

0.5400

0.5500

0.4850

$$v_{2}$$

The average number of eggs laid by a female adult green lacewings in one time step

7.2789

5.8237

2.3876 