On nonstandard chemotactic dynamics with logistic growth induced by a modified complex Ginzburg–Landau equation

Abstract

AbstractIn 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 , say with , and a nonstandard chemical production–degradation mechanism involving first‐ and second‐order derivatives of the logarithm of the cell density, say with , via the ()‐hydrodynamical system associated with a modified Ginzburg–Landau equation governing the evolution of the complex wavefunction . In a chemotactic context, 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.