CODES FOR APPROXIMATING LYAPUNOV EXPONENTS

We present a suite of codes for approximating Lyapunov exponents of nonlinear differential systems by so-called QR methods. The basic solvers perform integration of the trajectory and approximation of the Lyapunov exponents simultaneously. That is, they integrate for the trajectory at the same time, and with the same underlying schemes, as integration for the Lyapunov exponents is carried out. Separate codes solve small systems for which we can compute and store the Jacobian matrix, and fir large systems for which the Jacobian matrix cannot be stored, and it may not even be explicitly known. If it is known, the user has the option to provide its action on a vector An alternative strategy is also presented in which one may want to approximate the trajectory with a specialized solve,; linearize around the computed trajectory, and then carry out the approximation of the Lyapunov exponents using codes fir linear problems.