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My question is in regards to systems of ordinary differential equations. One of my research topics right now involves working with some complicated coupled ODEs used to model ecological stuff. Without getting into the details, the model I am working on now has a bad tendency to diverge for some initial conditions. I have thought and searched for a while now, but have been unable to come up with some good ways of determining when a system of ODEs will have certain solutions that diverge. Does anyone know of some literature or techniques that might be useful for me? I would very much appreciate any help you could provide. Thank you very much.

EDIT:

To avoid further misunderstanding, the type of equations I am considering are of the form:

[tex] \frac{d X_i}{dt} = F_i(\mathbf{X)} [/tex]

When I say that a solution diverges, I mean that given a set of initial conditions, the solution will diverge in time. As for what I mean by diverge, I mean that solutions tend to infinity as t approaches infinity. So solutions that settle in on a point, or go through some oscillatory behavior, even chaotic oscillatory behavior, would be considered non-divergent.

EDIT:

To avoid further misunderstanding, the type of equations I am considering are of the form:

[tex] \frac{d X_i}{dt} = F_i(\mathbf{X)} [/tex]

When I say that a solution diverges, I mean that given a set of initial conditions, the solution will diverge in time. As for what I mean by diverge, I mean that solutions tend to infinity as t approaches infinity. So solutions that settle in on a point, or go through some oscillatory behavior, even chaotic oscillatory behavior, would be considered non-divergent.

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