is it posible to model and predict the behavior of an ecosystem?

From what I've read they are chaotic systems and close to impossible to model.

If you can what sort of mathematics would you require to do so?

(sorry, if this belong to the maths forum,I thought it would involve more ecology)

A good first start is to look at the "predator prey model", which is a really simple model for a system where there are just 2 animals: a predator and a prey.

 

Modeling an ecosystem can be as complicated as you want. I've just given you the name of the most simple one. But obviously, if you plan on including 1000 species, and make geology part of your model, and perhaps include bacteria and the odd virus, you're gonna need a lot of time.

If you can what sort of mathematics would you require to do so?

(sorry, if this belong to the maths forum,I thought it would involve more ecology)

 

Systems of differential equations, qualitative theory of differential equations, complex systems, stochastic processes... It depends what exactly you're interested in, but if you want to make a career in theoretical/mathematical ecology, it's really a good place to be right now.

o.k.

seems like a logical thing to do .......

I'll start really really basic.Do you happen to know where I could get some data about populations in an area ,species diversity( and it's change over time),keystone species populations and movement,energy input (solar insolation),forest cover,etc.

Solar insolation I know a decent site: http://www.apricus.com/html/insolation_levels_europe.htm

For the other topics I'm afraid I have no decent source myself (I'd have to google just like anyone else).

thanks .I'll see if I can find sources (or better someone with first hand stats).