2008/12/07 by József Z. Farkas, Jozsef Z. Farkas, Thomas Hagen +1 · 30 citations
Mathematics · Medicine · Social Sciences · #Applied mathematics #Evolutionary Game Theory and Cooperation #Exponential growth #Exponential stability #Instability #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Nonlinear system #Physics #Population #Semigroup #Stochastic processes and statistical mechanics #math.AP #msc:35B35 #msc:47D06 #msc:92D25
paper · pdf · doi:10.3934/cpaa.2009.8.1825
published in Communications on Pure & Applied Analysis 8(6), 1825-1839 (American Institute of Mathematical Sciences)
arxiv created 2008/12/07 · openalex publication_date 2009/01/01 · arxiv updated 2019/03/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this work we consider asize-structured cannibalism model with the model ingredients(fertility, growth, and mortality rate) depending on size(ranging over an infinite domain) and on ageneral function of the standing population (environmentalfeedback). Our focus is on the asymptotic behavior of thesystem, in particular on the effect of cannibalism on the long-termdynamics. To this end, we formally linearize the system aboutsteady state and establish conditions in terms of the modelingredients which yield uniform exponential stability of the governing linear semigroup.We also show how the point spectrum of the linearized semigroup generatorcan be characterized in the special case of a separable attackrate and establish a general instability result.Further spectral analysis allows us to give conditions forasynchronous exponential growth of the linear semigroup.