TY - JOUR
T1 - An optimization framework of biological dynamical systems
AU - Horie, Ryota
PY - 2008/7/7
Y1 - 2008/7/7
N2 - Different biological dynamics are often described by different mathematical equations. On the other hand, some mathematical models describe many biological dynamics universally. Here, we focus on three biological dynamics: the Lotka-Volterra equation, the Hopfield neural networks, and the replicator equation. We describe these three dynamical models using a single optimization framework, which is constructed with employing the Riemannian geometry. Then, we show that the optimization structures of these dynamics are identical, and the differences among the three dynamics are only in the constraints of the optimization. From this perspective, we discuss the unified view for biological dynamics. We also discuss the plausible categorizations, the fundamental nature, and the efficient modeling of the biological dynamics, which arise from the optimization perspective of the dynamical systems.
AB - Different biological dynamics are often described by different mathematical equations. On the other hand, some mathematical models describe many biological dynamics universally. Here, we focus on three biological dynamics: the Lotka-Volterra equation, the Hopfield neural networks, and the replicator equation. We describe these three dynamical models using a single optimization framework, which is constructed with employing the Riemannian geometry. Then, we show that the optimization structures of these dynamics are identical, and the differences among the three dynamics are only in the constraints of the optimization. From this perspective, we discuss the unified view for biological dynamics. We also discuss the plausible categorizations, the fundamental nature, and the efficient modeling of the biological dynamics, which arise from the optimization perspective of the dynamical systems.
KW - Constrained optimization
KW - Hopfield neural networks
KW - Lotka-Volterra equation
KW - Replicator equation
KW - Riemannian geometry
UR - http://www.scopus.com/inward/record.url?scp=44749089828&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=44749089828&partnerID=8YFLogxK
U2 - 10.1016/j.jtbi.2008.02.029
DO - 10.1016/j.jtbi.2008.02.029
M3 - Article
C2 - 18423493
AN - SCOPUS:44749089828
VL - 253
SP - 45
EP - 54
JO - Journal of Theoretical Biology
JF - Journal of Theoretical Biology
SN - 0022-5193
IS - 1
ER -