Skip to Main content Skip to Navigation
Journal articles

Doubly nonlocal reaction-diffusion equations and the emergence of species

Abstract : The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one describes reproduction with different phenotypes. Linear stability analysis of the homogeneous in space stationary solution is carried out. Existence of travelling waves is proved in the case of narrow kernels of the integrals. Periodic travelling waves are observed in numerical simulations. Existence of stationary solutions in the form of pulses is shown, and transition from periodic waves to pulses is studied. In the applications to the speciation theory, the results of this work signify that new species can emerge only if they do not have common offsprings. Thus, it is shown how Darwin's definition of species as groups of morphologically similar individuals is related to Mayr's definition as groups of individuals that can breed only among themselves.
Document type :
Journal articles
Complete list of metadata

Cited literature [36 references]  Display  Hide  Download
Contributor : Vitaly Volpert Connect in order to contact the contributor
Submitted on : Saturday, November 19, 2016 - 4:58:48 PM
Last modification on : Tuesday, May 3, 2022 - 3:14:04 PM
Long-term archiving on: : Tuesday, March 21, 2017 - 12:02:39 PM


Files produced by the author(s)



Malay Banerjee, Vitali Vougalter, Vitaly Volpert. Doubly nonlocal reaction-diffusion equations and the emergence of species. Applied Mathematical Modelling, Elsevier, 2017, 42, pp.591-599. ⟨10.1016/j.apm.2016.10.041⟩. ⟨hal-01399589⟩



Record views


Files downloads