Traveling waves for a three-component reaction–diffusion model of farmers and hunter-gatherers in the Neolithic transition

2021 ◽  
Vol 82 (4) ◽  
Author(s):  
Sheng-Chen Fu ◽  
Masayasu Mimura ◽  
Je-Chiang Tsai
Keyword(s):  
Diffusion Model ◽  
Traveling Waves ◽  
Reaction Diffusion ◽  
Hunter Gatherers ◽  
Neolithic Transition ◽  
Reaction Diffusion Model ◽  
Three Component Reaction

scholarly journals Conditional symmetries and exact solutions of a nonlinear three-component reaction-diffusion model

2020 ◽  
pp. 1-21
Author(s):  
R. M. CHERNIHA ◽  
V. V. DAVYDOVYCH
Keyword(s):  
Asymptotic Behaviour ◽  
Exact Solutions ◽  
Reaction Diffusion ◽  
Hunter Gatherers ◽  
Classical Symmetry ◽  
Classical Symmetries ◽  
Reaction Diffusion Model ◽  
Three Component Reaction ◽  
Biological Interpretation ◽  
First Time

Abstract Q-conditional (non-classical) symmetries of the known three-component reaction-diffusion (RD) system [K. Aoki et al. Theor. Popul. Biol. 50, 1–17 (1996)] modelling interaction between farmers and hunter-gatherers are constructed for the first time. A wide variety of Q-conditional symmetries are found, and it is shown that these symmetries are not equivalent to the Lie symmetries. Some operators of Q-conditional (non-classical) symmetry are applied for finding exact solutions of the RD system in question. Properties of the exact solutions (in particular, their asymptotic behaviour) are identified and possible biological interpretation is discussed.

On the well-posedness of a dispersal model for farmers and hunter–gatherers in the Neolithic transition

2017 ◽  
Vol 28 (02) ◽  
pp. 195-222 ◽  
Author(s):  
Ján Eliaš ◽  
M. Humayun Kabir ◽  
Masayasu Mimura
Keyword(s):  
Temporal Evolution ◽  
Reaction Diffusion ◽  
Well Posedness ◽  
Hunter Gatherers ◽  
Neolithic Transition ◽  
Modelling Framework ◽  
Rate Of Spread ◽  
Reaction Diffusion Model ◽  
Hunting And Gathering ◽  
Spatio Temporal

We study the reaction–diffusion model that consists of equations that govern the spatio-temporal evolution of sedentary and migrating farmers and hunter–gatherers in the Neolithic transition. Ecologically, the model stems from the fact that a lifestyle of agriculture and settlement, as it allows for a larger population, is evolutionary advantageous than hunting and gathering. Therefore, in our modelling framework, we assume that farmers do not migrate unless the population density pressure forces them. We prove the global well-posedness of the system and, in contrast to the previous modelling work on the transition from hunting and gathering to farming, we show numerically that for a suitable value of a “stay-or-migrate” threshold the model is capable of reproducing the rate of spread of farming that corresponds to the archaeological findings in Europe.

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