# How to find conditional Lyapunov exponents

For a synchronized ODE system,I wanted to know if there is a program code in MATLAB available for plotting the conditional Lyapunov exponent. For example, synchronization of identical Rossler system with a coupling term $F$ present in both the response and the driver.The $F$ is not a coefficient of any variable. This is where I have a problem.

• Do we have to include the coupling in the jacobian matrix and if yes how?
• How to plot the Lyapunov exponent as a function of different values of $F$?

Thank you for any help.

• Can you explain what a "synchronized ODE system" is? – David Ketcheson Jan 19 '12 at 6:04
• Well,in the case of Rossler system if the response asymptotically follows the dynamics of the driver in the presense of an external coupling term F,then the system (response+driver) is said to be identically synchronized. – SKM Jan 22 '12 at 8:02
• Can you provide the equations or a link? – David Ketcheson Jan 22 '12 at 13:32
• The synchronization has to be done,i mean the system has to be constructed with the appropriate controller.I found this link for calculating lyapunov exponent for the unsynchronized case :mathworks.com/matlabcentral/fileexchange/… . I am trying to modify this code for the synchronized case. Upon synchronization,we take into consideration only the response system. So,in the program we shall have the sameset of equations but one of the equation will have an external forcing term say 5*F where F is a sine wave(for my case).How to calculate J? – SKM Jan 22 '12 at 20:40