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Bifurcations in a modulation equation for alternans in a cardiac fiber

Shu Dai, David G. Schaeffer (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as discordant alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. As shown in our previous paper, the zero solution of their equation may lose...

Bilinear system as a modelling framework for analysis of microalgal growth

Štěpán Papáček, Sergej Čelikovský, Dalibor Štys, Javier Ruiz (2007)

Kybernetika

A mathematical model of the microalgal growth under various light regimes is required for the optimization of design parameters and operating conditions in a photobioreactor. As its modelling framework, bilinear system with single input is chosen in this paper. The earlier theoretical results on bilinear systems are adapted and applied to the special class of the so-called intermittent controls which are characterized by rapid switching of light and dark cycles. Based on such approach, the following...

Biochemical network of drug-induced enzyme production: Parameter estimation based on the periodic dosing response measurement

Volodymyr Lynnyk, Štěpán Papáček, Branislav Rehák (2021)

Kybernetika

The well-known bottleneck of systems pharmacology, i. e., systems biology applied to pharmacology, refers to the model parameters determination from experimentally measured datasets. This paper represents the development of our earlier studies devoted to inverse (ill-posed) problems of model parameters identification. The key feature of this research is the introduction of control (or periodic forcing by an input signal being a drug intake) of the nonlinear model of drug-induced enzyme production...

Blowup solutions to Keller-Segel system and its simplified systems

Takasi Senba (2006)

Banach Center Publications

In this paper, we will consider blowup solutions to the so called Keller-Segel system and its simplified form. The Keller-Segel system was introduced to describe how cellular slime molds aggregate, owing to the motion of the cells toward a higher concentration of a chemical substance produced by themselves. We will describe a common conjecture in connection with blowup solutions to the Keller-Segel system, and some results for solutions to simplified versions of the Keller-Segel system, giving the...

Blow-up versus global existence of solutions to aggregation equations

Grzegorz Karch, Kanako Suzuki (2011)

Applicationes Mathematicae

A class of nonlinear viscous transport equations describing aggregation phenomena in biology is considered. General conditions on an interaction potential are obtained which lead either to the existence or to the nonexistence of global-in-time solutions.

Boundedness and stabilization in a three-dimensional two-species chemotaxis-Navier-Stokes system

Hirata, Misaki, Kurima, Shunsuke, Mizukami, Masaaki, Yokota, Tomomi (2017)

Proceedings of Equadiff 14

This paper is concerned with the two-species chemotaxis-Navier–Stokes system with Lotka–Volterra competitive kinetics ( 1 ) t + u · 1 = 𝔻 1 - χ 1 · ( 1 c ) + μ 1 1 ( 1 - 1 - a 1 2 ) in × ( 0 , ) , ( 2 ) t + u · 2 = 𝔻 2 - χ 2 · ( 2 c ) + μ 2 2 ( 1 - a 2 1 - 2 ) in × ( 0 , ) , c t + u · c = 𝔻 c - ( α 1 + β 2 ) c in × ( 0 , ) , u t + ( u · ) u = 𝔻 u + P + ( γ 1 + 2 ) Φ , · u = 0 in × ( 0 , ) under homogeneous Neumann boundary conditions and initial conditions, where is a bounded domain in R3 with smooth boundary. Recently, in the 2-dimensional setting, global existence and stabilization of classical solutions to the above system were first established. However, the 3-dimensional case has not been studied: Because of difficulties in the Navier–Stokes system, we can...

Boundedness in a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source

Ji Liu, Jia-Shan Zheng (2015)

Czechoslovak Mathematical Journal

We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of Cao (2014).

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