System of Differential Equations

PhDP
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Hello,

I'll take a research course very soon, and I would like to analyse the behavior of some system of differential equations (with sometime up to 6 differential equations). To do so, I would need a good book.

I'm not interested in long mathematical proofs, I just want to have a good book to use as a reference to analyse the behavior of such system rigorously.

BTW, I finished my 3 introductionary courses in Calculus, + multivariable calculus and a course on differential equations... and the research is in biology.

Thx
 
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There's so many books on dynamical system, it's hard to choose :)
 
Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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