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Page 8891 of Mathematical Reviews Vol. , Issue 2001M
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2001
Mathematical Reviews
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-uniform asymptotic stability of the trivial solution for the initial-boundary value problem to the following semilinear reaction-diffusion system with delay:
Ou; (x, t) = ma oa = d;(t)Au;(x, t) + S > ...
The main theorem proved is that, under certain conditions on the reaction param- eters/diffusivities of the model, if the Hopf bifurcation on the two-dimensional local center manifold for the system without ...
Page 5498 of Mathematical Reviews Vol. , Issue 2001H
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2001
Mathematical Reviews
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. = 0, h > 0, ¢>0, x € (0,L), with assigned initial conditions and two types of boundary conditions, namely (I) Neumann conditions on v and clamped ends for w, (II) Dirichlet boundary conditions on v and ...
For a significant class of nonlin- ear equations it is shown that an unstable equilibrium solution of the reaction-diffusion system cannot be stabilized by the introduc- tion of delay. ...
Front and Turing patterns induced by Mexican-hat–like nonlocal feedback
2015
Europhysics letters
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2014 pre-print arXiv:1411.6561v1 fatcat:am3vwsgccbgnlpufrlfedb66omOther Versions
We consider the effects of a Mexican-hat-shaped nonlocal spatial coupling, i.e., symmetric long-range inhibition superimposed with short-range excitation, upon front propagation in a model of a bistable ...
This behaviour is investigated through a linear stability analysis of the spatially homogeneous steady states and numerical investigations of the full nonlinear equations in dependence upon the nonlocal ...
-This work was supported by DFG in the framework of SFB 910 "Control of selforganizing nonlinear systems." ...
doi:10.1209/0295-5075/109/40014
fatcat:o73sqbprk5hdfl7mqfp6d7ecxi
Page 5155 of Mathematical Reviews Vol. , Issue 2003g
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2003
Mathematical Reviews
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Additionally, nonlocal spatial effects are present because of the combination of delay and diffusion. ...
A. (4-SUR-MS; Guildford)
Linear and nonlinear stability in a diffusional ecotoxicological model with time delays. (English summary)
Discrete Contin. Dyn. Syst. Ser. B 2 (2002), no. 4, 575-590. ...
Pattern formation in a coupled membrane-bulk reaction-diffusion model for intracellular polarization and oscillations
[article]
2019
arXiv
pre-print
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Here we study the distribution of the polarity protein Cdc42 in a mass-conserved membrane-bulk model, and explore the effects of diffusion and spatial dimensionality on spatio-temporal pattern formation ...
We then extend our analysis to a two-dimensional (2-D) model, for which species can either diffuse inside the cell or become bound to the membrane and undergo a nonlinear reaction-diffusion process. ...
BX is supported by the Robert and Sara Lumpkins Endowment for Postdoctoral Fellows in Applied and Computational Math and Statistics at the University of Notre Dame. ...
arXiv:1910.10203v1
fatcat:edo6srywkjephczhhngjuolh2e
Dynamics of reaction-diffusion patterns controlled by asymmetric nonlocal coupling as a limiting case of differential advection
2014
Physical Review E
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A one-component bistable reaction-diffusion system with asymmetric nonlocal coup ling is derived as limiting case of a two-component activator-inhibitor reaction -diffusion model with differential advection ...
The effects of asymmetric nonlocal couplings in such a bistable reaction-diffusi on system are then compared to the previously studied case of a system with symm etric nonlocal coupling. ...
ACKNOWLEDGMENT We acknowledge financial support from the German Science Foundation DFG in the framework of SFB 910 "Control of Self-Organizing Nonlinear Systems." ...
doi:10.1103/physreve.89.052909
pmid:25353863
fatcat:dmr7e2nf7rehrbe7xvzc67lszy
Page 9188 of Mathematical Reviews Vol. , Issue 2003m
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2003
Mathematical Reviews
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Summary: “We introduce a general method for the systematic derivation of nonlinear reaction-diffusion equations with dis- tributed delays. ...
In order to make a connection with the transport models used in the literature, we make transformations which eliminate the transition time and derive a set of nonlocal equations which are nonlinear generalizations ...
Nonlocal control of pulse propagation in excitable media
2014
European Physical Journal B : Condensed Matter Physics
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As a generic example for an excitable medium the FitzHugh-Nagumo model with diffusion in the activator variable is considered. ...
It is shown that one can observe these effects for various choices of the integral kernel and the coupling scheme, provided that the control strength and spatial extension of the integral kernel is appropriate ...
This work was supported by DFG in the framework of SFB 910 "Control of self-organizing nonlinear systems". Helpful discussions with Julien Siebert are gratefully acknowledged. ...
doi:10.1140/epjb/e2014-50339-2
fatcat:usm76calknfmtmvgfiqtmw67ba
Numerical algorithms for solving the optimal control problem of simple bioreactors
2019
Nonlinear Analysis: Modelling and Control
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The dynamics of this device is described by a system of two nonstationary nonlinear diffusion–convection–reaction equations. ...
The second aim of this paper is to solve the inverse problem and to determine optimal boundary conditions. These results enable us to estimate the potential accuracy of the proposed devices. ...
The authors would like to thank referees for their comments, which are helpful and constructive, and Prof. J. Janno for the fruitful discussions on ill-posedness of the obtained inverse problems. ...
doi:10.15388/na.2019.4.8
fatcat:7hcjqu3gmff4rhzec3kj5dkqwi
Control of sub-excitable waves in neural networks by nonlocal coupling
[article]
2007
arXiv
pre-print
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To investigate this process, we use a reaction-diffusion system of inhibitor-activator type as a generic model of pathological wave propagation and set it close to bifurcation in the sub-excitable regime ...
We report the influence of various nonlocal connectivity schemes on wave propagation. ...
Acknowledgments This work has been partially supported by the DFG within the framework of Sfb 555 and the Sachbeihilfe DA-602/1-1. ...
arXiv:0707.4619v1
fatcat:r553dtzfmret7cuuqf3cvpfwwu
Page 1860 of Mathematical Reviews Vol. , Issue 88d
[page]
1988
Mathematical Reviews
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The authors study the hyperbolicity of stationary solutions of the scalar reaction-diffusion equation u, = Au+ f(u) with Dirichlet boundary conditions on a ball in R”. ...
The reaction mechanism in this model is affected by time delays, and the coupling of the equations is through the interface of the two compartments. ...
Page 1928 of Mathematical Reviews Vol. , Issue 2000c
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2000
Mathematical Reviews
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The authors study stability conditions for a uniform stationary so- lution of an equation of the form u, = f(u,v)+ Dux. with D> 0, x € [0,1], and no flux boundary conditions. ...
A. (4-SUR-MS; Guildford) Linear stability criteria in a reaction-diffusion equation with spatially inhomogeneous delay. (English summary) Dynam. Stability Systems 14 (1999), no. 1, 71-91. ...
Nonlocal Reaction–Diffusion Model of Viral Evolution: Emergence of Virus Strains
2020
Mathematics
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The model consists of a nonlocal reaction–diffusion equation for the virus density depending on the genotype considered to be a continuous variable and on time. ...
This equation contains two integral terms corresponding to the nonlocal effects of virus interaction with host cells and with immune cells. ...
Conflicts of Interest: The authors declare no conflict of interest. ...
doi:10.3390/math8010117
fatcat:wqo4clqs7ndark2jmrdznpngce
Spiral Waves in Nonlocal Equations
2005
SIAM Journal on Applied Dynamical Systems
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An unexpected result is that the boundaries seem to play a much more significant role in determining stability and rotation speed of spirals, as compared with reaction-diffusion systems having only local ...
This type of equation has been previously studied as a model for large scale pattern formation in the cortex and involves spatially nonlocal interactions through a convolution. ...
I thank the referees for their useful comments, which I feel have improved the paper. ...
doi:10.1137/040612890
fatcat:3oojesdb6bfzjdnxss6zolsjmm
Page 15 of Mathematical Reviews Vol. , Issue 2002G
[page]
2002
Mathematical Reviews
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A reaction-diffusion model of single population growth with time delay is considered. ...
the spectrum and regularized trace of the Sturm-Liouville problem with spectral parameter on the boundary condition and with the operator coefficient. ...
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