A penetrating analysis of the wave dynamic modes of a conceptual population system described by the ’reaction-taxis-diffusion’ and ’reaction-autotaxis-cross-diffusion’ polynomial models is carried out for the case of increasing degrees of the reaction and taxis (autotaxis) functions. It is shown that a ’suitable’ nonlinear taxis can affect the wave front sets and generate nonmonotone waves, such as trains and pulses which represent the exact solutions of the model system. Parametric critical points whose neighborhood displays the full spectrum of possible model wave regimes are identified and a wave mode systematization in the form of bifurcation diagrams is given. This enables standard criteria of approach to ’dangerous boundaries’ to be developed. As possible applications, ’pulsing density patches’ in forest insect populations as well as plankton communities and some other examples are discussed.

PACS: 05.45.−a, 87.10.+e, 87.23.Cc (all) DOI: 10.1070/PU1999v042n09ABEH000564 URL: https://ufn.ru/en/articles/1999/9/d/ 000083399000004 Citation: Berezovskaya F S, Karev G P "Bifurcations of travelling waves in population taxis models" Phys. Usp. 42 917–929 (1999) BibTexBibNote ® (generic) BibNote ® (RIS)MedlineRefWorks TY JOUR TI Bifurcations of travelling waves in population taxis models AU Berezovskaya, F. S. AU Karev, G. P. PB Physics-Uspekhi PY 1999 JO Physics-Uspekhi JF Physics-Uspekhi JA Phys. Usp. VL 42 IS 9 SP 917-929 UR https://ufn.ru/en/articles/1999/9/d/ ER https://doi.org/10.1070/PU1999v042n09ABEH000564 Оригинал: Березовская Ф С, Карев Г П «Бифуркации бегущих волн в популяционных моделях с таксисом» УФН 169 1011–1024 (1999); DOI: 10.3367/UFNr.0169.199909d.1011