Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources

By S. Génieys, Vitaly Volpert, P. Auger. 2006

218 citations recorded by the source corpus.

Subfields: Genetics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/b5ae72b51b7205e3307e3cad90b29ede539bd4c2

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In Genetics

In Modeling and Simulation

In Public Health, Environmental and Occupational Health

Citations in the corpus

Generalized Transition Waves and Their Properties (2010, unknown): “in [2, 10, 14, 15, 16, 21, 22]).”
Super-linear spreading in local and non-local cane toads equations (2015, background): “We also note that in general non-local Fisher-KPP type equations the stability of the steady state u ≡ 1 may fail [5, 20, 21].”
On selection dynamics for continuous structured populations (2008, methodology): “A first case has been studied by Genieys, Volpert and Auger in [11], They show that in the case where a(x)=1, the steady solution f̄ =1 is unstable as soon as the Fourier transform of b is not positive.”
The non-local Fisher–KPP equation: travelling waves and steady states (2009, methodology): “This model was also investigated numerically in [1, 9, 11], and numerical simulations exhibit a much richer behavior than the aforementioned rigorous perturbative results close to σ = 0 indicate.”
On the existence of stationary solutions for some non-Fredholm integro-differential equations (2011, background): “Keywords: solvability conditions, non Fredholm operators, integro-differential equations, stationary solutions AMS subject classification: 35J10, 35P30, 35K57”
Dirac Mass Dynamics in Multidimensional Nonlocal Parabolic Equations (2010, unknown): “This avoids the branching patterns that are usual in this kind of models [17, 22, 26, 27].”
Travelling Waves in a Nonlocal Reaction-Diffusion Equation as a Model for a Population Structured by a Space Variable and a Phenotypic Trait (2012, background): “Therefore, we shall need an extra work to catch the behavior (12) as x → + .”
Modeling Complex Systems (2010, unknown): “ûij (t; z) = ĥij (x (t; z)) ; j = 1; :::;m for all i: (15)”