A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
Filters
Modern Perspectives on Near-Equilibrium Analysis of Turing Systems
[article]
2021
arXiv
pre-print
Preserved Fulltext
Other Versions
framework, including evolving and complex manifolds, systems heterogeneous in space and time, and more general reaction-transport equations. ...
Here we review modern developments in the mathematical theory pioneered by Turing, showing how his approach has been generalized to a range of settings beyond the classical two-species reaction-diffusion ...
in heterogeneous environments. ...
arXiv:2106.08375v2
fatcat:os5dbssjafeydhpo4gkwclqogi
Dirichlet problem for a diffusive logistic population model with two delays
2018
Discrete and Continuous Dynamical Systems. Series S
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
In this paper, we investigate a diffusive logistic equation with nonzero Dirichlet boundary condition and two delays. ...
Furthermore, we prove global stability of the positive steady state under certain conditions and obtain global Hopf bifurcation results. ...
When Ω is bounded, various boundary conditions can be imposed, which include Dirichlet boundary condition, Neumann boundary condition, and Robin boundary condition. ...
doi:10.3934/dcdss.2020134
fatcat:kj5aket2ynfjrdbdiibrbbxuee
Time-delay effect on a diffusive predator–prey model with habitat complexity
2021
Advances in Difference Equations
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
AbstractBased on the predator–prey system with a Holling type functional response function, a diffusive predator–prey system with digest delay and habitat complexity is proposed. ...
In addition, the calculation formulas of the bifurcation direction and the stability of bifurcating periodic solutions are derived. ...
Availability of data and materials Data sharing not applicable to this article as no datasets were generated or analysed during the current study. ...
doi:10.1186/s13662-021-03473-y
fatcat:l274tq74vfhf7gg7jhjrnswlei
Periodic travelling waves in cyclic populations: field studies and reaction-diffusion models
2008
Journal of the Royal Society Interface
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2008; you can also visit the original URL.
The file type is application/pdf.
Mathematical modelling has a major role to play in understanding these results and informing future empirical studies. ...
We describe the notion of a wave family, and various ecologically relevant scenarios in which periodic travelling waves occur. ...
Periodic travelling wave generation by boundaries with hostile environments When an ecological habitat is surrounded by a hostile environment, the appropriate boundary condition is of Robin type, vu=vx ...
doi:10.1098/rsif.2007.1327
pmid:18211865
pmcid:PMC2408372
fatcat:um77m3i52fdxpdcimo277wy2u4
The Pattern Formation of an Urban System
2010
Geographical Analysis
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
To investigate the stability of the system, we will perform a linear stability analysis of equations (5) and (6) with boundary conditions. ...
“Theory of the Diffusion of Price Inflation in an Imperfect Market Similar to Housing, Having Delayed Arbitrage.” Environment and Planning A 11, 1219-29.
Wilson, A. G. (1981). ...
doi:10.1111/j.1538-4632.1988.tb00164.x
fatcat:n7u4heyk4ngxfoext4gtw6pqna
The influence of density in population dynamics with strong and weak Allee effect
2021
Journal of the Egyptian Mathematical Society
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. ...
When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. ...
Kamrujjaman research was partially supported by the Ministry of Science and Technology (MOST), Grant BS193 for year 2019-2020, Bangladesh. ...
doi:10.1186/s42787-021-00114-x
fatcat:pqsrdb5bvvgilft6wllsatpwsy
2019 Index IEEE Transactions on Automatic Control Vol. 64
2019
IEEE Transactions on Automatic Control
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2020; you can also visit the original URL.
The file type is application/pdf.
., +, TAC Oct. 2019 4024-4034 Feedback Stabilization of a 1-D Linear Reaction-Diffusion Equation With Delay Boundary Control. ...
., +, TAC Oct. 2019 4024-4034 Feedback Stabilization of a 1-D Linear Reaction-Diffusion Equation With Delay Boundary Control. ...
doi:10.1109/tac.2020.2967132
fatcat:o2hd2t4jz5fbpkcemjt5aj7xrm
Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping
[article]
2023
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2023; you can also visit the original URL.
The file type is application/pdf.
Other Versions
Most generally, these models take the form of nonlocal reaction-diffusion-advection equations, where the nonlocality may appear in the spatial domain, the temporal domain, or both. ...
This review paper is expected to act as a synthesis of existing efforts while also pushing the boundaries of current modelling perspectives to better understand the influence of cognitive movement mechanisms ...
on reaction-advection-diffusion equations. ...
arXiv:2201.09150v3
fatcat:waqrecymnfemroogog6gwqkslu
Partial differential equations for self-organization in cellular and developmental biology
2008
Nonlinearity
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current ...
, and the new modelling opportunities that are emerging as a result. ...
A modelling framework for such systems via reaction-diffusion PDEs is ∂u ∂t = ∇ · (D∇u) + f(u, x, t), (21) on a bounded domain, usually with Neumann, Dirichlet or Robin boundary conditions. ...
doi:10.1088/0951-7715/21/11/r05
fatcat:e266xvcdfbcgxknyd2i54zshoq
Asymptotic periodicity of a food-limited diffusive population model with time-delay
2006
Journal of Mathematical Analysis and Applications
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
In this paper, a general reaction-diffusion food-limited population model with time-delay is proposed. ...
of the environment, and also take the effect of time-delay into consideration, based on Model-3 in [2], we can get a generalized reaction-diffusion model as follows: ...
Acknowledgment The authors thank the referee for her/his suggestions and comments on the paper and for bringing our attentions to some related references. ...
doi:10.1016/j.jmaa.2005.03.036
fatcat:mnkvz3efuney5fbj7tqjgvohzq
Dynamics of infectious diseases: A review of the main biological aspects and their mathematical translation
2021
Applied Mathematics and Nonlinear Sciences
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
In particular, some heterogeneity factors which could influence the fitting of the model to reality are pointed out. ...
In addition, some simulation techniques to validate a mathematical model and to estimate the model parameters are shown. ...
Mathematical models may effectively help in assessing various biological features to implement or suppress heterogeneities, control measures and environment conditions, that are key links in the dynamics ...
doi:10.2478/amns.2021.1.00012
fatcat:f2oeb6mkyjaj5nc3j2cfr5nvkq
2020 Index IEEE Transactions on Cybernetics Vol. 50
2020
IEEE Transactions on Cybernetics
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2021; you can also visit the original URL.
The file type is application/pdf.
., and Gao, H., Reference Trajectory Reshaping Optimi-zation and Control of Robotic Exoskeletons for Human-Robot Co-Manipulation; TCYB Aug. 2020 3740-3751 Wu, X., Jiang, B., Yu, K., Miao, c., and Chen, ...
., +, TCYB July 2020 3182-3194 Anti-Synchronization in Fixed Time for Discontinuous Reaction-Diffusion Neural Networks With Time-Varying Coefficients and Time Delay. ...
., +, TCYB July 2020 3125-3135 Anti-Synchronization in Fixed Time for Discontinuous Reaction-Diffusion Neural Networks With Time-Varying Coefficients and Time Delay. ...
doi:10.1109/tcyb.2020.3047216
fatcat:5giw32c2u5h23fu4drupnh644a
Meshless techniques for anisotropic diffusion
2014
Applied Mathematics and Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2018; you can also visit the original URL.
The file type is application/pdf.
Transport processes are common in geoscience applications, and find their way into models of, e.g., the atmosphere, oceans, shallow water, subsurface, seismic inversion, and deep earth. ...
A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability. ...
We present complex scenarios of multicomponent reactive transport in 2-D and in 3-D. These scenarios are further developments of the setting given by the MoMaS benchmark. ...
doi:10.1016/j.amc.2014.03.032
fatcat:c527226gyfgbffnq4p67qxd7wi
A Review of Multiscale Analysis: Examples from Systems Biology, Materials Engineering, and Other Fluid–Surface Interacting Systems
[chapter]
2005
Advances in Chemical Engineering
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
CTS-9702615, CTS-9811088, ITR-0219211, and CTS-0312117). The ideas on spatial coarse graining of the lattice MC method have been developed in collaboration with Prof. Markos A. Katsoulakis. ...
Proofreading by graduate students (Mark Snyder, Jeff Ludwig, Kapil Mayawala, and Dan Zak) of the University of Delaware is also greatly appreciated. ...
Furthermore, the boundary conditions in the BCF model ignore the discrete nature of steps and treat them as continuum points where either partial equilibrium or Robin boundary conditions are applied. ...
doi:10.1016/s0065-2377(05)30001-9
fatcat:qulpsmltmvdsrk4wpetev4gn3a
Threshold dynamics of a reaction-diffusion-advection Leslie-Gower predator-prey system
2022
Discrete and continuous dynamical systems. Series B
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
We study the large time behavior of solutions and establish threshold conditions for persistence and extinction of two species when they live in open advective environments. ...
<p style='text-indent:20px;'>In this paper, we investigate the global dynamics of a Leslie-Gower predator-prey system in advective homogeneous environments. ...
We should like to thank the anonymous referees for their careful readings of our manuscript and the useful comments made for its improvement. ...
doi:10.3934/dcdsb.2021260
fatcat:yw7ax2qdkrbhrcmwh647x3azr4
« Previous
Showing results 1 — 15 out of 244 results