Appendix I. Stability analysis of two-plant model without plant growth limitation (text equations 5 and 6).


The Jacobean matrix of partial derivatives for equations (5) and (6) is:



Substituting equations (9) and (10), the values of s and n at equilibrium yield:



The eigenvalues for this matrix were evaluated by solving for L in:



Using the formula for roots of the quadratic equation, the eigenvalues were found to be:


L1, L2 =


The real part of the eigenvalues (rμ/bc) is always positive.  Therefore the two plant model without plant growth limitation is unstable, as suggested by graphical analysis.