Problem with ODE solvers

I want to numerically solve the following system of diff. eqns:

dx/dt = y
dy/dt = z
dz/dt = -y + x^2 - 0.025

where d is a constant.

The initial point is [0.5,0.5,0.5]

I have tried both stiff and nonstiff ODE solvers to no avail. The system always diverges to huge values and the following error pops up:

"Warning: Failure at t=2.660704e+00. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (7.105427e-15) at time t."

I have tried changing the eps value but it is not of much help.

A theoretical analysis shows that the system should not diverge. What do you guys suggest I do? The code that I used:

function [x,y,z] = system2(d ,initV, T, eps)
%       d       - system paramter
%       INITV   - initial point
%       T       - time interval
%       EPS     - ode solver precision
%
% Example.
%        [X Y Z] = system2(1, [1.5 1.5 1.5], [0 25], 0.000001);
%        plot3(X,Y,Z);

if nargin<2
  eps = 0.000001;
  T = [0 25];
  initV = [1.5 1.55 1.5];
end

options = odeset('RelTol',eps,'AbsTol',[eps eps eps/100]);
[T,X] = ode23tb(@(T,X) F(T, X, d), T, initV, options);

plot3(X(:,1),X(:,2),X(:,3));
axis equal;
grid;
title('System2');
xlabel('X'); ylabel('Y'); zlabel('Z');

x = X(:,1);
y = X(:,2);
z = X(:,3);
return
end

function dx = F(T, X, d)

      dx = zeros(3,1);
      dx(1) = X(2);
      dx(2) = X(3);
      dx(3) = -X(2) + X(1)^2 - d;

      return
  end

Answer 1

[Amit]

What theoretical analysis you did which says that this does not diverges?

To me, this will diverge as the size of x goes bigger. Your initial value is > 1 for all X. There is no terms in all 3 differentials, that will keep it in bound. dX(3) will grow very fast (X(1)^2 will dominate very soon). This will make dX(2) grow bigger, making dx(1) bigger.