Title :
Analytic computation of the integrated response in nonlinear reaction-diffusion systems
Author :
Lopez-Caamal, Fernando ; Garcia, Miriam R. ; Oyarzun, Diego A. ; Middleton, R.H.
Author_Institution :
Hamilton Inst., Nat. Univ. of Ireland Maynooth, Maynooth, Ireland
Abstract :
In this work we analytically derive the time-integral of a class of nonlinear reaction-diffusion systems commonly found in networks of biochemical reactions. This formula is inferred using the Laplacian Spectral Decomposition method, which approximates the solution of the Partial Differential Equations by a finite series capturing the most relevant dynamics. The time-integrals allow us to understand how signal transmission depends on initial and boundary conditions, spatial geometry and the turnover rates of some species.
Keywords :
biochemistry; cellular biophysics; nonlinear systems; partial differential equations; reaction-diffusion systems; signal processing; Laplacian spectral decomposition method; analytic computation; biochemical reaction networks; boundary conditions; finite series capture; integrated response; nonlinear reaction-diffusion systems; partial differential equations; signal transmission; spatial geometry; turnover rates; Boundary conditions; Equations; Hilbert space; Jacobian matrices; Kinetic theory; Laplace equations; Vectors;
Conference_Titel :
Decision and Control (CDC), 2012 IEEE 51st Annual Conference on
Conference_Location :
Maui, HI
Print_ISBN :
978-1-4673-2065-8
Electronic_ISBN :
0743-1546
DOI :
10.1109/CDC.2012.6426397