Invading the ideal free distribution
A boundary value problem for integrodifference population models with cyclic kernels
December 2014, 19(10): 3209-3218. doi: 10.3934/dcdsb.2014.19.3209
Persistence and extinction of diffusing populations with two sexes and short reproductive season
Wen Jin 1, and Horst R. Thieme 2,
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287-1804, United States
School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287
Received June 2013 Revised October 2013 Published October 2014
A model is considered for a spatially distributed population of male and female individuals that mate and reproduce only once in their life during a very short reproductive season. Between birth and mating, females and males move by diffusion on a bounded domain $\Omega$. Mating and reproduction is described by a (positively) homogeneous function (of degree one). We identify a basic reproduction number $\mathcal{R}_0$ that acts as a threshold between extinction and persistence. If $\mathcal{R}_0 <1$, the population dies out while it persists (uniformly weakly) if $\mathcal{R}_0 > 1$. $\mathcal{R}_0$ is the cone spectral radius of a bounded homogeneous map.
Keywords: cone spectral radius, discrete dynamical system, Impulsive reaction diffusion system, ordered Banach space, two-sex population, stability., discrete semiflow, basic reproduction number, eigenvector, homogeneous map, difference equation.
Mathematics Subject Classification: Primary: 39A70, 35B99, 92D25; Secondary: 39A6.
Citation: Wen Jin, Horst R. Thieme. Persistence and extinction of diffusing populations with two sexes and short reproductive season. Discrete & Continuous Dynamical Systems - B, 2014, 19 (10) : 3209-3218. doi: 10.3934/dcdsb.2014.19.3209
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Wen Jin Horst R. Thieme