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Cross-diffusion driven instability in a predator-prey system with cross-diffusion
[article]
2014
arXiv
pre-print
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In this work we investigate the process of pattern formation induced by nonlinear diffusion in a reaction-diffusion system with Lotka-Volterra predator-prey kinetics. ...
Finally when the pattern invades the domain as a travelling wavefront, we derive the Ginzburg-Landau amplitude equation which is able to describe the shape and the speed of the wave. ...
The kinetics is of the Lotka-Volterra predator-prey type with a logistic term for the preys: R and K are the growth rate and carrying capacity for the prey, respectively, M is the predator death rate, ...
arXiv:1311.1748v4
fatcat:3bzmthkmmre7zm36hs5kjexdse
Turing instability and traveling fronts for a nonlinear reaction–diffusion system with cross-diffusion
2012
Mathematics and Computers in Simulation
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Recently it has been proposed a three-species model [30] with linear diffusion that, in the appropriate limit [11] , shows convergence to (1.1). ...
When the size of the spatial domain is large, and the initial perturbation is localized, the pattern is formed sequentially and invades the whole domain as a traveling wavefront. ...
See also the interesting model in [22] where the system (1.1) is coupled with a transport law, and [19] . type given in (1.1), the simple Lotka-Volterra kinetics is sufficient to generate patterns. ...
doi:10.1016/j.matcom.2011.11.004
fatcat:wlocgzkhrnabjfyf6tx6gut6km
Pattern formation driven by cross-diffusion in a 2D domain
2013
Nonlinear Analysis: Real world applications
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2012 pre-print arXiv:1211.4412v1 fatcat:dzgoynso7vdsngvnlqhdhadz4q
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. ...
However, if the model has a trivializing kinetics, as it is the case for competitive Lotka-Volterra kinetics, classical diffusion is not sufficient to destabilize the equilibria, no matter what the diffusion ...
Lotka-Volterra, i.e. all γ ij > 0. ...
doi:10.1016/j.nonrwa.2012.11.009
fatcat:fmi5zgzwcren7n7m6czwe5kmk4
Model on cell movement, growth, differentiation and de-differentiation: Reaction-diffusion equation and wave propagation
2013
The European Physical Journal E : Soft matter
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can switch from a steady propagating wavefront to the interesting situation of propagation of a faster wavefront with a slower waveback. ...
With different cell types labeled by state variables, the model can be formulated in terms of the associated transition probabilities between various states. ...
Such a "switch of gear" phenomenon has also been recently produced in the population dynamics of competitive Lotka-Volterra model with spatial diffusion [48] .
Appendix A. ...
doi:10.1140/epje/i2013-13065-4
pmid:23807466
fatcat:v6mydrn37fen5i5hjhkuezui54
Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
[article]
2024
arXiv
pre-print
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Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue ...
Nonlocality is important in realistic mathematical models of physical and biological systems at small-length scales. It characterizes the properties of two individuals located in different locations. ...
This research was enabled in part by support provided by SHARCNET and the Digital Research Alliance of Canada. ...
arXiv:2401.14651v1
fatcat:dxm4ky6xgzeuvhm6x7nfvd5ciy
Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping
[article]
2023
arXiv
pre-print
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Mathematical rules of thumb are provided to judge the model rationality, to aid in model development or interpretation, and to streamline an understanding of the range of difficulty in possible model conceptions ...
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 ...
A special thank you to Sophia Salmaniw for painting the graphics used in Figure 1 . ...
arXiv:2201.09150v3
fatcat:waqrecymnfemroogog6gwqkslu
Prey-taxis and its applications
2006
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with permission of the copyright owner. ...
, loan, distribute and sell theses worldwide, for com mercial or non com mercial purposes, in microform, paper, electronic and/or any other formats. ...
Independently, a chemotaxis advection term was introduced into the Lotka-Volterra equations by Pettet and McElwain [75] to describe angiogenesis and wound healing. ...
doi:10.7939/r3-gtrd-j098
fatcat:mnpivglj6jgxbnked7vwzm7lf4
The role of fluctuations in ecological patterns and processes
2015
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The five years in Padova were instrumental for the development of my forma mentis and the School played a big part in it. I am grateful to my friends and colleagues ...
To my family and mentors bachelor and master studies, set the foundations for my choice of pursuing an interdisciplinary PhD and allowed me to get into contact with Andrea Rinaldo, Amos Maritan, and many ...
Since my first visit to EPFL and Eawag in May 2011 it was clear that I had a great opportunity in front of me, and it proved to be so. ...
doi:10.5075/epfl-thesis-6541
fatcat:l3oag3yerrhg7mcu5v3x6q3qgi