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)

HOST-PARASITOID- DELAY DIFFERENTIAL EQUATIONS WITH DISTRIBUTED DELAY

I swear I will write this all up and explain better. Notes: 1) Take with a grain of salt- still working on this 2) Parasitoid attack is based on a type II functional response 3) Converted DDEs into a system of ODES using the LINEAR CHAIN TRICK