On nonstandard chemotactic dynamics with logistic growth induced by a modified complex Ginzburg–Landau equation
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Wiley Online Library
Materia
Chemotaxis Keller–Segel system Modified complex Ginzburg– Landau equation Modulational stability Solitary wave Solito
Date
2021-08-22Referencia bibliográfica
López JL. On nonstandard chemotactic dynamics with logistic growth induced by a modified complex Ginzburg–Landau equation. Stud Appl Math. 2021;1–22. [https://doi.org/10.1111/sapm.12440]
Sponsorship
Junta de Andalucia European Commission PY18-RT-2422 and AFQM-311-UGR18; MINECO-Feder (Spain)Abstract
In this paper, we derive a variant of the classical Keller-Segel model of chemotaxis incorporating a growth term of logistic type for the cell population n(t,x), say nu n(1-n) with nu>0, and a nonstandard chemical production-degradation mechanism involving first- and second-order derivatives of the logarithm of the cell density, say f lambda ab(n,nx,nxx)=lambda n+anxxn+bnx2n2 with lambda,a,b is an element of R, via the (n,S)-hydrodynamical system associated with a modified Ginzburg-Landau equation governing the evolution of the complex wavefunction psi=neiS. In a chemotactic context, S(t,x) will play the role of the concentration of chemical substance. Then, after carrying out a detailed analysis of the modulational stability of uniform-in-space plane waves, dark soliton-shaped traveling wave densities of the former system are constructed from solitary wave solutions of the latter.