abbii42
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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?
I've tried literally everything i can think of to solve the equations (I'm not going to put it all down here but suffice to say i got nowhere). But I'm not actually sure i should be solving them at all. If i estimate as a linear system I'm fairly sure I could solve it, that's not the problem, it's whether or not that would give me the answer i need.
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?
I've tried literally everything i can think of to solve the equations (I'm not going to put it all down here but suffice to say i got nowhere). But I'm not actually sure i should be solving them at all. If i estimate as a linear system I'm fairly sure I could solve it, that's not the problem, it's whether or not that would give me the answer i need.