Re: Can anyone send me the folliwing paper?

rams wrote:

could you tell me what is the "jacobian matrix" for the
above discrete system .....

http://en.wikipedia.org/wiki/Jacobian

The Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function. Its importance lies in the fact that it represents the best linear approximation to a differentiable function near a given point. In this sense, the Jacobian is akin to a derivative of a multivariate function.

how to find the max lyapunov exponent of the
above system .

http://en.wikipedia.org/wiki/Lyapunov_exponent#Numerical_calculation

Read it yourself. It helps.
.