论文信息 - Reaction-Diffusion Systems as Complex Networks

Reaction-Diffusion Systems as Complex Networks

The spatially distributed reaction networks are indispensable for the understanding of many important phenomena concerning the development of organisms, coordinated cell behavior, and pattern formation. The purpose of this brief discussion paper is to point out some open problems in the theory of PDE and compartmental ODE models of balanced reaction-diffusion networks.

[1] Jacquelien M. A. Scherpen,et al. Explicit simplicial discretization of distributed-parameter port-Hamiltonian systems , 2012, Autom..

[2] Arjan van der Schaft,et al. On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics , 2011, SIAM J. Appl. Math..

[3] N. Rashevsky,et al. Mathematical biology , 1961, Connecticut medicine.

[4] Jacquelien M. A. Scherpen,et al. Hamiltonian perspective on compartmental reaction-diffusion networks , 2012, Autom..

[5] A. Schaft,et al. Discrete exterior geometry approach to structure-preserving discretization of distributed-parameter port-Hamiltonian systems , 2011, 1111.6403.

[6] A. M. Turing,et al. The chemical basis of morphogenesis , 1952, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences.

[7] Jeff Morgan. Global Existence for Semilinear Parabolic Systems on One-dimensional Bounded Domains , 1991 .

[8] J. Morgan,et al. Stability and Lyapunov functions for reaction-diffusion systems , 1997 .

[9] David F. Anderson,et al. A Proof of the Global Attractor Conjecture in the Single Linkage Class Case , 2011, SIAM J. Appl. Math..