Qualitative Analysis of Spruce Budworm Outbreaks 5/6/2019 Qualitative Analysis of Spruce Budworm Outbreaks by Ron Bassar

Fast Slow Budworms Surface area of Predators Branches Energy Reserve Divide variables into fast and slow categories Fast Slow Budworms Surface area of Predators Branches Energy Reserve

Budworm Growth Equation

Finding Equilibrium Points

B=0 is an Equilibrium Point

Dimensionless Parameters

Dimensionless Variable

Dimensionless Means No Units

Grouping of Parameters in the Equation

Sub in Dimensionless Parameters

5/6/2019 Per Capita Death and Growth Rates in Terms of the Dimensionless Variables

Predation and Growth Curves Plotted vs. Budworm Density

R Increases to Point Where G and H Coalesce

Equilibria disappear as R increases and Budworm Population jumps to I

If R Decreases Population Remains at I

Still at I

Population Jumps to G as R Continues to Decrease

Bifurcation Curves

Equations of Branch Surface Area and Energy Reserve 5/6/2019 Equations of Branch Surface Area and Energy Reserve

Equilibrium Points of S and E

Analysis of Slow Variables