mirzaevinom / steadystateapproximation

A numerical framework for computing approximations to stationary solutions of general evolution equations

Steady-State Approximation

This software package is distributed in the hope that it will be useful for the asymptotic analysis of size-structured population models. The theoretical framework for this software has been developed in Mirzaev I., and Bortz D.M., (2016), where we developed a numerical framework for computing approximations to stationary solutions of general evolution equations. This software can also be used to produce existence and stability regions for steady states of size-structured population models.

Two particular applications are given:

1. Population balance equations (see Mirzaev, I., & Bortz, D. M. (2015). arXiv:1507.07127 )
2. Sinko-Streifer size-structured population model (see Sinko, J. W., and Streifer, W. (1967), Ecology, 48(6):910-918. )

Dependencies

The program is written purely in Python 2.7. It depends on some famous libraries: SciPy, NumPy, matplotlib, multiprocessing, etc. All the dependencies can be solved by installing Anaconda software package. Installation instructions can be found at https://www.continuum.io/downloads

Basic Usage

For example to generate existence and stability regions for the population balance equations:

1. Navigate to the folder, where you have extracted this software package.
2. Change model rates in pbe_model_rates.py file as you desire (instructions available in the python file).
3. Run the following command in your terminal

 python pbe_exixtence_region.py 

Generated existence and stability regions can be found in images folder. Similarly, run programs pbe_jacobian_eigenvalue_plots.py and pbe_stability_plots.py

Note that to simulate Sinko-Streifer model. Model rates should be updated in sinko_model_rates.py and the program sinko_existence_region.py should be run according to above instructions.

Citation

If you use this program to do research that leads to publication, we ask that you acknowledge use of this program by citing the following in your publication::

Cite the paper:

Mirzaev I., Bortz D. M. (2016) A numerical framework for computing steady states of size-structured population models and their stability , arXiv:1602.07033

Cite the software package:

Mirzaev, I. (2016). Steady state approximation. https://github.com/MathBioCU/SteadyStateApproximation.

More Information

For further information please contact me at [email protected]