The delay Rosseler is
dx/dt=-y-z-a x(t-r),
dy/dt=x+by,
dz/dt=c+z (x-g),
this system has Chaotc attractor with a = 0.2, b =c = 0.2, g = 5.7, r = 2.0, and initial condition (0.1, 0.2, 0.3).
Is the next alternate representation of delay system in terms of N + 3 ordinary differential equations (ODEs) true or not?
dx1/dt= -xN+2 -xN+3 +a xN+1
dxi/dt= N(xi-1 – xi+1)/2r 2 ≤ i ≤ N
dxN+1/dt= N(xN – xN+1 )/r
dxN+2/dt=x1 + b xN+2
dxN+3/dt=c + xN+3 (x1 -g)
with initial conditions xi=0.1, 1 ≤ i ≤ N+1, xN+2 = 0.2, xN+3 =0.3.
the correct discrete form is :
x(i+1)-x(i)=N(-y(i)-z(i)-ax(i-r))
y(i+1)-y(i)=N(x(i)+by(i))
z(i+1)-z(i)=N(c+z(i)(x(i)-g))
when forward difference is used.
Dear Seyed
Thank you for your answer. But if r is fraction not integer what can I do?
Dear Dr. Paul Tobin
Thank you for your comment and your notes. Your notes talked about the relationship between Ordinary differential equations and Difference Equations. But my system is Delay differential Equation and I want to know how can I transform the delay differential equations to ODEs or Difference Equations. Many thanks for your time.
Ah, ok, speed reading has its disadvantages. I'll have a think about it
Regards
Paul
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