Tuesday, November 10, 2015
Mathematica: Linear Stability Analysis Symbolically
Trying to do a linear stability analysis of a 5 ODE system. Simple Egg -> Small Larvae -> Large Larvae -> Pupae-> Adult system (no delay and such)
Assumptions
1) Recruitment into a class is same throughout all classes
2) There is larval competition between the small larvae and the large larvae (density dependent death- symbolized by mu1)
3) There is natural background mortality that is symbolized by mu0)
This is just a symbolic analysis (not numerical).
So I wrote down the differential equations.
Equated the equations to 0.
Then solved for the system using Solve in Mathematica
I had three solutions.
I ignored the first solution.
Then I created a 5x5 Jacobian Matrix.
I put in the solved equations into the Jacobian Matrix then found the eigenvalues.
It seem that all the eigenvalues are negative and real (thus is stable)
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