Abstract
The modeling of a fully populated 3D tree able to regulate dynamically remains a relatively unexplored field. A non-dimensional representation of "autoregulation" coupled with an asymmetric binary tree algorithm has been developed. The tree has a defined topology as well as a spatial representation in 3D. An analysis using a simple linearization shows the systems dynamics when perturbed away from equilibrium. Results, based on previously published work by Karch and Schreiner are presented for a variety of parameters which provide different shapes of the tree and indicate a possible mechanism for "growing" the tree in specified directions. In addition the tree, through the use of local tagging has the ability to vary its size locally via a coupled set of conservation and reverting differential equations.
Original language | English |
---|---|
Pages (from-to) | 1464-1481 |
Number of pages | 18 |
Journal | Mathematics and Computers in Simulation |
Volume | 81 |
Issue number | 7 |
DOIs | |
Publication status | Published - 2011 |