Approximating state-space manifolds which attract solutions of systems of delay-differential equations Export

@article{citeulike:776587, abstract = {Although the theory of delay-differential equations (DDEs) is generally best set in a function space, some systems of DDEs have solutions which, after the decay of transients, lie on a low-dimensional manifold in their state space. When the delay is small, highly accurate approximations to the state-space manifold which attracts the solutions can be constructed by a simple functional equation treatment. This allows the reduction of the original system of DDEs to a smaller system of ordinary differential equations. The simplified model obtained may be used to facilitate bifurcation analysis. The method is applied to two biochemical models, namely to a delay-differential version of Michaelis\&\#150;Menten kinetics (the Brown model) and to a simple inducible operon model. \©1998 American Institute of Physics.}, author = {Roussel, Marc R.}, citeulike-article-id = {776587}, citeulike-linkout-0 = {http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JCPSA6000109000019008154000001&idtype=cvips&gifs=yes}, citeulike-linkout-1 = {http://link.aip.org/link/?JCP/109/8154}, citeulike-linkout-2 = {http://dx.doi.org/10.1063/1.477478}, doi = {10.1063/1.477478}, journal = {The Journal of Chemical Physics}, keywords = {mathematics}, number = {19}, pages = {8154--8160}, posted-at = {2006-07-27 19:45:08}, priority = {2}, publisher = {AIP}, title = {Approximating state-space manifolds which attract solutions of systems of delay-differential equations}, url = {http://dx.doi.org/10.1063/1.477478}, volume = {109}, year = {1998} }

TY - JOUR ID - citeulike:776587 L3 - citeulike-article-id:776587 N2 - Although the theory of delay-differential equations (DDEs) is generally best set in a function space, some systems of DDEs have solutions which, after the decay of transients, lie on a low-dimensional manifold in their state space. When the delay is small, highly accurate approximations to the state-space manifold which attracts the solutions can be constructed by a simple functional equation treatment. This allows the reduction of the original system of DDEs to a smaller system of ordinary differential equations. The simplified model obtained may be used to facilitate bifurcation analysis. The method is applied to two biochemical models, namely to a delay-differential version of Michaelis–Menten kinetics (the Brown model) and to a simple inducible operon model. ©1998 American Institute of Physics. IS - 19 JF - The Journal of Chemical Physics EP - 8160 TI - Approximating state-space manifolds which attract solutions of systems of delay-differential equations PB - AIP VL - 109 SP - 8154 KW - mathematics AU - Roussel, Marc PY - 1998/// UR - http://dx.doi.org/10.1063/1.477478 ER -