Software: LESLIS/LESLIL and LESNLS/LESNLL

This is a suite of Fortran 77 codes that approximate Lyapunov exponents of linear and nonlinear continuous dynamical systems.

There are four routines to approximate the Lyapunov exponents, depending on which problem you have:

LESLIL: LInear Large

LESLIS: LInear Small

LESNLL: NonLinear Large

LESNLS: NonLinear Small


The naming "large" and "small" is for convenience and for typical use.


In "large", there are programs which never need to store (possibly, not even know) the Jacobian, the coefficient matrix in the linear case. They require the action (Jacobian)x(vector) =: J*v


In the nonlinear case, this can be computed in a Jacobian free way, whereby the action J*v is approximated by discrete directional derivatives internally by the code. Alternatively, the user may provide the action J*v analytically. See documentation of LESNLL.


For the "linear large" codes, LESLIL, the user must provide the action A(t)*v analytically in a subroutine, see documentation and sample drivers.


For the "linear small" option, the codes require explicit storage (and knowledge) of the Jacobian, the coefficient matrix, in the linear case. For small problems, say of dimension up to 10, when forming and storing the Jacobian is not a hindrance, this is the recommended way to proceed since it is more efficient.


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Authors:
Luca Dieci, <dieci@math.gatech.edu>, and Erik S. Van Vleck, <evanvleck@math.ku.edu>



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These codes are provided for the benefit of the scientific community. While the authors decline any responsibility for possible malfunctioning of the codes, they will welcome any and all comments on bugs and the like. Please report any mishap to the first named author above.

If you use these codes, the authors would appreciate your acknowledging having done so in the reports, publications, theses, etc., resulting from their use.

The authors gratefully acknowledge the support of the National Science Foundation (NSF) during the time period in which these codes were written.



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To use the codes, save the relevant zip file(s) below in the directory where you are going to put the codes.




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Linear Codes:

For example, say you save the file for the linear codes, that will be "linear.zip" below. Upon saving the file, type "unzip -a linear.zip", and then you will see that a directory called "linear" with subdirectories "small" and "large" was created. Moving inside one of these subdirectories, it will be evident how to proceed.



Zipped file containing the codes for linear problems: LESLIS, LESLIL and auxiliary routines.

Accompanying Technical Report for the Linear Codes.



Non Linear Codes:

Just as for the linear codes, if you save the file for the nonlinear codes, that will be "nonlinear.zip" below. Upon saving the file, type "unzip -a nonlinear.zip", and then you will see that a directory called "nonlinear" with subdirectories "small" and "large" was created. Moving inside one of these subdirectories, it will be evident how to proceed.



Zipped file containing the codes for nonlinear problems: LESNLS, LESNLL and auxiliary routines.

See also the related paper Numerical techniques for approximating Lyapunov exponents and their implementation [With M. Jolly, E. Van Vleck. In Journal of Computational and Nonlinear Dynamics 6-1 (Jan 2011).]