Analytical proofs in mathematical papers

[marellasunny]

I am writing my first paper in applied mathematics.I would like to know how important is it to write a analytical proof for the numerical solutions arrived?I always thought these sort of things were left to the 'pure mathematicians' and one didn't need to bother.As a engineer,I was always used to substituting into formulae and arriving at solutions :). But,now that I write a paper for a journal,should I make it more theoretical?

This is what I am writing my paper on:

I am making a mathematical model of a ecological system.I use a system of non-linear differential equations to model the system.These equations involve parameters.On modelling these system of equations numerically in MATLAB ,I arrive at "surfaces with folds" i.e cusps,elliptic umbilics etc. Should I arrive at a mathematical-analytical proof to explain the reason for the shapes of these surfaces?Do I even need to for a applied math paper?

 

[Studiot]

If you wish to include such material I would suggest an appendix rather than inclusion in the main body of the text.

 

[marellasunny]

I hope I am not misleading with the term 'analytical proof'.I meant it in the pure math sense.The reason I have this doubt is because I am writing a mathematical biology paper and it wouldn't make sense to include MATLAB programs in the paper,rather a mathematical proof would give the reader a straight idea as to what the system is and how it would behave if varied.So,I ask again,would it make sense to include a mathematical proof(already in existence) and a few lines of the author's mathematical understanding of the subject in a 'mathematical biology' paper?
Thanks

 

[Stephen Tashi]

Look at other papers published in the journal you are sumitting your paper to. See what type of expositions the editors of the journal have accepted.