A Preliminary Coupled Quorum Sensing–Chemotaxis–Flocking Framework for Oil Field Bacterial Collective Motion

Bacterial collective behaviour emerges from the interplay of three distinct dynamical processes: quorum sensing (QS) mediates density-dependent gene regulation, chemotaxis directs movement along chemical gradients, and flocking aligns individual trajectories into coherent group motion. While each process has been studied extensively in isolation, no unified framework has integrated all three into a single mathematical model. Here, we present a deterministic coupled ordinary differential equation (ODE) and partial differential equation (PDE) framework that links QS-mediated phenotypic switching to Cucker–Smale flocking and Keller–Segel chemotaxis. Our mean-field reduction reveals a saddle-node bifurcation in the quorum-sensing-to-flocking transition: when the autoinducer concentration crosses a critical threshold, bacteria switch from fast, disordered, chemotactically driven planktonic motion (i.e., bacterial swimming, 2–2.5 μm/s (bulk)) to slow or fast, highly aligned, aggregation-prone swarm behaviour (5 ± 2 μm/s) and further to aggregation and biofilm-associated sessibility. Numerical simulations of the agent-based ODE model show that this switch drives spontaneous aggregation at chemoattractant sources, with flocking order peaking before the QS transition and collapsing as clusters form. A spatially resolved PDE–ODE hybrid confirms that autoinducer fields develop localized hotspots that coincide with bacterial aggregates, creating a positive feedback loop between density, signalling, and cohesion. Bifurcation analysis identifies a hysteresis region where small perturbations in basal autoinducer production can trigger hysteric transitions between planktonic and sessile states. These results provide a mechanistic basis for the well-documented but poorly understood motility–sessility switch in bacteria such as Pseudomonas aeruginosa and establish a quantitative platform for engineering synthetic microbial consortia with programmed collective behaviours.