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has been cited by the following article:

• TITLE: Pattern Formations in Bacteria-Biosurfactant Interactions of Microbial Enhanced Oil Recovery

  AUTHORS: Sadrack Dingaonaro Mokein, Sali Issa, Saidou Abdoulkary, Alidou Mohamadou, Henri Paul Ekobena Fouda

  KEYWORDS: Two Specie Models, Predator-Prey Models, Pattern Formations, Spatial Diffusion

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.11, November 10, 2025

  ABSTRACT: This paper investigates the dynamic interactions between biosurfactant-producing bacteria and their environment through pattern formations in diffusive predator-prey models. By analyzing the model’s equilibrium points and applying the Routh-Hurwitz criteria with bifurcation analysis, we determine the conditions for the existence of Turing patterns. Numerical simulations confirm these analytical findings and reveal diverse pattern formations influenced by diffusion and concentration zones, including both Turing and non-Turing patterns. We observe a correlation between the distribution of the two species through pattern formations and the effectiveness of biosurfactant-mediated oil recovery. More interestingly, our model focuses on the dynamics of bacterial and biosurfactant concentrations by showing that areas of high biosurfactant concentration are associated with the release of trapped oil from pores, thereby contributing to successful oil recovery.