Propagation of second order integrodifference equations with local monotonicity. (English) Zbl 1218.39005
The authors study the following integrodifference equation
\[ u_{n+1}(x)= \int_\mathbb R k(x- y)b(u_n(y), u_{n-1}(y))\,dy,\quad n= 0,1,2,\dots.\tag{*} \]
In population dynamics, (*) is describing the age-structure model, where \(u_n(x)\) is the population density at time \(n\) at position \(x\in\mathbb R\), \(b:\mathbb R^2\to\mathbb R^+\) is a continuous function formulating the reproduction of the species and \(k\) is a probability function reflecting the spatial migration of the individuals. The spreading speed and traveling wave solutions of (*) are investigated.
\[ u_{n+1}(x)= \int_\mathbb R k(x- y)b(u_n(y), u_{n-1}(y))\,dy,\quad n= 0,1,2,\dots.\tag{*} \]
In population dynamics, (*) is describing the age-structure model, where \(u_n(x)\) is the population density at time \(n\) at position \(x\in\mathbb R\), \(b:\mathbb R^2\to\mathbb R^+\) is a continuous function formulating the reproduction of the species and \(k\) is a probability function reflecting the spatial migration of the individuals. The spreading speed and traveling wave solutions of (*) are investigated.
Reviewer: Jurang Yan (Taiyuan)
MSC:
| 39A12 | Discrete version of topics in analysis |
| 45J05 | Integro-ordinary differential equations |
| 92D25 | Population dynamics (general) |
Keywords:
integrodifference equation; age-structure model; spreading speeds; traveling wave solution; propagation mode; auxiliary equation; local monotonicity; population dynamicsReferences:
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