The effect of density-dependent dispersal on the stability of populations

Mulone, G.; Rionero, Salvatore; Wang, W.

doi:10.1016/j.na.2011.04.055

Cited by 12 publications

(7 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The analytical description of this phenomenon will be the subject of a forthcoming paper. It would be also of interest to rigorously prove that, when the chemotactic coefficient is below the threshold, the disease-free equilibrium is globally asymptotically stable, using the techniques adopted, e.g., in [19,20,[23][24][25].…”

Section: Numerical Simulations and Discussionmentioning

confidence: 99%

Wavefront invasion for a chemotaxis model of Multiple Sclerosis

et al. 2016

View full text Add to dashboard Cite

In this work we study wavefront propagation for a chemotaxis reactiondiffusion system describing the demyelination in Multiple Sclerosis. Through a weakly non linear analysis, we obtain the Ginzburg-Landau equation governing the evolution of the amplitude of the pattern. We validate the analytical findings through numerical simulations. We show the existence of traveling wavefronts connecting two different steady solutions of the equations. The proposed model reproduces the progression of the disease as a wave: for values of the chemotactic parameter below threshold, the wave leaves behind a homogeneous plaque of apoptotic oligodendrocytes. For values of the chemotactic coefficient above threshold, the model reproduces the formation of propagating concentric rings of demyelinated zones, typical of Baló's sclerosis.

show abstract

Section: Numerical Simulations and Discussionmentioning

confidence: 99%

Wavefront invasion for a chemotaxis model of Multiple Sclerosis

et al. 2016

View full text Add to dashboard Cite

show abstract

“…System (2) belongs to a large class of models involving density depending diffusion (see e.g. [23]) or cross-diffusion to reproduce segregation effects and the creation of spatial niches [19,26,24]. Cross-diffusion terms should be introduced when the gradient of the density of one species induces a flux of another species.…”

Section: Introductionmentioning

confidence: 99%

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

2014

View full text Add to dashboard Cite

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.

show abstract

“…Nevertheless, in many experimental cases, the gradient of the density of one species induces a flux of another species or of the species itself, therefore nonlinear effects should be taken into account. Recently, nonlinear diffusion terms have appeared to model different physical phenomena in diverse contexts like population dynamics and ecology [12,29,34,15,14,16,33,26], and chemical reactions [3,22].…”

Section: Introductionmentioning

confidence: 99%

Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion

2014

View full text Add to dashboard Cite

In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel-Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear diffusion intensifies the tendency to pattern formation; in particular, unlike the case of classical linear diffusion, the Turing instability can occur even when diffusion of the inhibitor is significantly slower than activator's one. In the Turing pattern region we perform the WNL multiple scales analysis to derive the equations for the amplitude of the stationary pattern, both in the supercritical and in the subcritical case. Moreover, we compute the complex Ginzburg-Landau equation in the vicinity of the Hopf bifurcation point as it gives a slow spatio-temporal modulation of the phase and amplitude of the homogeneous oscillatory solution.

show abstract

The effect of density-dependent dispersal on the stability of populations

Cited by 12 publications

References 14 publications

Wavefront invasion for a chemotaxis model of Multiple Sclerosis

Wavefront invasion for a chemotaxis model of Multiple Sclerosis

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

Turing Instability and Pattern Formation for the Lengyel–Epstein System with Nonlinear Diffusion

Contact Info

Product

Resources

About