Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion

Marco Maria Luigi Sammartino, Maria Carmela Lombardo, Sammartino, Lombardo, Tulumello

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11 Citazioni (Scopus)

Abstract

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. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. 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.
Lingua originaleEnglish
pagine (da-a)621-633
Numero di pagine13
RivistaActa Applicandae Mathematicae
Volume132
Stato di pubblicazionePublished - 2014

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Predator prey systems
Cross-diffusion
Predator-prey System
Amplitude Equations
Nonlinear analysis
Nonlinear Analysis
Landau Equation
Traveling Wavefronts
Lotka-Volterra
Predator-prey
Ginzburg-Landau Equation
Nonlinear Diffusion
Spatial Pattern
Wavefronts
Pattern Formation
Reaction-diffusion System
Kinetics
Predict
Numerical Simulation
Computer simulation

All Science Journal Classification (ASJC) codes

  • Applied Mathematics

Cita questo

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abstract = "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. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. 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.",
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T1 - Cross-Diffusion Driven Instability in a Predator-Prey System with Cross-Diffusion

AU - Sammartino, Marco Maria Luigi

AU - Lombardo, Maria Carmela

AU - Sammartino, null

AU - Lombardo, null

AU - Tulumello, null

PY - 2014

Y1 - 2014

N2 - 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. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. 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.

AB - 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. We show that the cross-diffusion term is responsible of the destabilizing mechanism that leads to the emergence of spatial patterns. Near marginal stability we perform a weakly nonlinear analysis to predict the amplitude and the form of the pattern, deriving the Stuart-Landau amplitude equations. Moreover, in a large portion of the subcritical zone, numerical simulations show the emergence of oscillating patterns, which cannot be predicted by the weakly nonlinear analysis. 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.

UR - http://hdl.handle.net/10447/96937

M3 - Article

VL - 132

SP - 621

EP - 633

JO - Acta Applicandae Mathematicae

JF - Acta Applicandae Mathematicae

SN - 0167-8019

ER -