Robust feed-back control of travelling waves in a class of reaction–diffusion distributed biological systems

Vilas, Carlos; García, Míriam R.; Banga, Julio R.; Alonso, Antonio A.

doi:10.1016/j.physd.2008.02.019

Cited by 26 publications

(10 citation statements)

References 40 publications

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“…We choose the basis as orthonormal eigenfunctions of the Laplacian, i.e. subject to the boundary conditions [11]. The time-integrals are then with coefficientsand .…”

Section: Resultsmentioning

confidence: 99%

Cumulative Signal Transmission in Nonlinear Reaction-Diffusion Networks

et al. 2013

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Quantifying signal transmission in biochemical systems is key to uncover the mechanisms that cells use to control their responses to environmental stimuli. In this work we use the time-integral of chemical species as a measure of a network’s ability to cumulatively transmit signals encoded in spatiotemporal concentrations. We identify a class of nonlinear reaction-diffusion networks in which the time-integrals of some species can be computed analytically. The derived time-integrals do not require knowledge of the solution of the reaction-diffusion equation, and we provide a simple graphical test to check if a given network belongs to the proposed class. The formulae for the time-integrals reveal how the kinetic parameters shape signal transmission in a network under spatiotemporal stimuli. We use these to show that a canonical complex-formation mechanism behaves as a spatial low-pass filter, the bandwidth of which is inversely proportional to the diffusion length of the ligand.

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“…We choose the basis as orthonormal eigenfunctions of the Laplacian, i.e. subject to the boundary conditions [11]. The time-integrals are then with coefficientsand .…”

Section: Resultsmentioning

confidence: 99%

Cumulative Signal Transmission in Nonlinear Reaction-Diffusion Networks

et al. 2013

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“…37 This scheme employs the proper orthogonal decomposition method to obtain a low-dimensional approximation of the system and designs the feedback controller. 37 This scheme employs the proper orthogonal decomposition method to obtain a low-dimensional approximation of the system and designs the feedback controller.…”

Section: Discussionmentioning

confidence: 99%

Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh–Nagumo model

Konishi

Takeuchi

Shimizu

2011

Chaos

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Elimination and control of nonlinear phenomena in excitable media are important for academic interests and practical applications. This paper provides a systematic procedure to design external forces for eliminating a traveling wave in a one-dimensional piecewise linear FitzHugh-Nagumo model. This procedure allows us to design nonfeedback and feedback control systems. The feedback control systems are designed using classical control theory. Furthermore, this procedure is extended to a two-dimensional model and verified using numerical simulation.

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“…The differences among each particular technique lie in the computation of the spatial dependent functions (also known as basis functions) f i j ðzÞ which will define the FDS. In this section we concentrate on the proper orthogonal decomposition (POD) technique which has proved to be a very efficient technique for the simulation of high dimensional PDE problems in several fields (Berkooz et al, 1993;Balsa-Canto et al, 2002;García et al, 2007;Vilas et al, 2008). In POD, the basis functions (also known as empirical basis functions or POD basis) are computed through an optimization problem.…”

Section: Simulation Via the Proper Orthogonal Decomposition Methodsmentioning

confidence: 99%

Combination of multi-model predictive control and the wave theory for the control of simulated moving bed plants

Vilas¹,

Wouwer²

2011

Chemical Engineering Science

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Robust feed-back control of travelling waves in a class of reaction–diffusion distributed biological systems

Cited by 26 publications

References 40 publications

Cumulative Signal Transmission in Nonlinear Reaction-Diffusion Networks

Cumulative Signal Transmission in Nonlinear Reaction-Diffusion Networks

Design of external forces for eliminating traveling wave in a piecewise linear FitzHugh–Nagumo model

Combination of multi-model predictive control and the wave theory for the control of simulated moving bed plants

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