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 |