Nonlinear systems of differential equations

[abbii42]

I think I posted in the wrong section and will repost in the textbook/coursework section but don't know how to delete this. Although if you want to answer feel free.

The complete question I've been given:
The Rossler equations are formally defined as
dx/dt=−y−z
dy/dt=x+ay
dz/dt=b+z(x−c).
Let us suppose that a=0.2, b=0.2, c=5.7, x(0)=y(0)=z(0)=0, t∈[0,400].
Let v1(t) be the solution to the given initial value problem, and let v2(t) be the solution of the initial value problem with x(0)=0.001, y(0)=z(0)=0. Please find (analytically an estimate of the value of tmax>0 such that |v1(t)-v2(t)|<=1 for all t∈[0,tmax]. You may assume that max{|x(t)|,|y(t)|,|z(t)|}<=25 for all t.

Do I need to actually solve the equations and if so how?
If i don't then what do I need to do? would approximating the system by a linear one be in the right direction?

 

[gtoguy97]

Yes, you need to solve the equations in order to estimate the value of tmax. One approach to solving the equations would be to use numerical methods such as Euler's method or Runge-Kutta. Alternatively, you could approximate the system by a linear one (e.g. using the Taylor series expansion), which may make it easier to solve.