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

In this paper, we derive a variant of the classical Keller–Segel model chemotaxis incorporating growth term logistic type for cell population , say with and nonstandard chemical production–degradation mechanism involving first- second-order derivatives logarithm density, via ()-hydrodynamical system associated modified Ginzburg–Landau equation governing evolution complex wavefunction . chemotactic context, will play role concentration substance. Then, after carrying out detailed analysis modulational stability uniform-in-space plane waves, dark soliton-shaped traveling wave densities former are constructed from solitary solutions latter.