TY - JOUR
T1 - Inverse Eigenvalue Problems for Exploring the Dynamics of Systems Biology Models
AU - Lu , James
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 711
EP - 728
PY - 2009
DA - 2009/01
SN - 1
DO - http://doi.org/10.4208/aamm.09-m09S04
UR - https://global-sci.org/intro/article_detail/aamm/8393.html
KW - Inverse eigenvalue problems, dynamical systems, bifurcation, biology, sparsity.
AB - <p style="text-align: justify;">This paper describes inverse eigenvalue problems that arise in
studying qualitative dynamics in systems biology models. 
An
algorithm based on lift-and-project iterations is proposed, where the lifting step entails solving a constrained matrix inverse 
eigenvalue problem. In particular, prior to carrying out the iterative steps, $a$-$priori$ bounds on 
the entries of the Jacobian matrix are computed by relying on the reaction network structure as well as the form of 
the rate law expressions for the model under consideration. Numerical results on a number of models show that the proposed 
algorithm can be used to computationally explore the possible dynamical scenarios while identifying the important 
mechanisms via the use of sparsity-promoting regularization.</p>