Databases: Network Population Models

Networks have become a popular way to concisely represent complex nonlinear systems where the interactions and parameters are
imprecisely known. One challenge is how to best describe the associated dynamics, which can exhibit
complicated behavior sensitive to small changes in parameters. A recently developed computational
approach that we refer to as a database for dynamics provides a robust and mathematically rigorous description of
global dynamics over large ranges of parameter space. To demonstrate the potential of this approach
we consider two classical age-structured population models that share the same network diagram and have a similar nonlinear overcompensatory term, but nevertheless yield different patterns of qualitative behavior as a function of parameters.
Using a generalization of these models we relate the different structure of the dynamics that are observed in the context of
biologically relevant questions such as stable oscillations in populations, bistability, and permanence.

All of the files on this page along with the Database Explorer software (Mac only) can be downloaded in a single zip file here. This contains both Morse database files (*.mdb) with no Conley index information, full Conley-Morse database files (*.cmdb) including all computed Conley index information. Version 1.0 of the Database Explorer will open the 2-d parameter space computations while version 2.0 is required for the 3-d computation. Each version is placed in the appropriate folder in the zip file. A guide for interpreting the output of the Database Explorer can be found on this page.

The following tables summarize the important information about each of the computations. Information about time is for a run on a cluster with 16 nodes, each sharing 128GB of memory among 32 processors.

The database software used to produce these files can be downloaded here.

Parameter Space |
Parameter Space Depth |
Phase Space |
Phase Space Min Depth |
Phase Space Max Depth |
Phase Space Initial |
Size Limit |
Morse Process Time (s) |
Conley Process Time (s) |
Data |

7 | 24 | 32 | 1 | 10000 | 3789 | 1419 |
Intermediate-0.0
CMG and Conley Indices |
||

7 | 24 | 32 | 1 | 10000 | 6778 | 3475 |
Intermediate-0.01
CMG and Conley Indices |
||

7 | 24 | 32 | 1 | 10000 | 9728 | 3810 |
Intermediate-0.02
CMG and Conley Indices |
||

7 | 24 | 32 | 1 | 10000 | 26310 | 3853 |
Intermediate-0.05
CMG and Conley Indices |
||

7 | 24 | 32 | 1 | 10000 | 42974 | 5219 |
Intermediate-0.1
CMG and Conley Indices |
||

7 | 24 | 32 | 1 | 10000 | 4920 |
Intermediate-1.0
CMG and Conley Indices |

This table contains a database run on the full 3-d parameter space. The variable

This computation was performed with version 2.0 of the database software.

Parameter Space |
Parameter Space Depth |
Phase Space |
Phase Space Min Depth |
Phase Space Max Depth |
Phase Space Initial |
Size Limit |
Morse Process Time (s) |
Conley Process Time (s) |
Data |

θ_{1},θ_{2}: 5 s': 6 |
24 | 32 | 1 | 10000 |
Intermediate-3d
CMG and Conley indices |