Journal of Modern Chemistry & Chemical Technology Original Research
Artificial Intelligence–Driven Optimal Control of Limit Cycle Oscillations in Active Colloidal Systems
Abstract
Active colloidal droplets driven by Marangoni stresses exhibit complex nonlinear interfacial dynamics including spontaneous symmetry breaking, self-propulsion, and oscillatory instability behavior. In this work, a reduced-order nonlinear dynamical framework is developed for an active spherical colloidal droplet with surfactant-driven interfacial transport. Starting from the coupled Stokes flow, convection–diffusion–reaction, and interfacial stress balance equations, a Galerkin projection is applied to derive a three-mode reduced-order model governing the dominant surfactant concentration dynamics on the droplet interface. The resulting nonlinear ordinary differential equation system captures the essential coupling between interfacial surfactant transport, Marangoni forcing, and chemical activity. Numerical continuation and bifurcation analysis using MATCONT reveal the existence of Hopf bifurcation points and associated limit-cycle oscillations, demonstrating the onset of self-sustained oscillatory interfacial behavior. The first Lyapunov coefficient indicates a subcritical Hopf bifurcation characterized by unstable oscillatory dynamics and bistability. An optimal-control problem is then formulated in Pyomo, with the activity parameter serving as the time-dependent control variable The proposed control strategy successfully suppresses oscillatory behavior by steering the system away from instability regions. The developed framework provides a computationally tractable methodology for integrating reduced-order modeling, bifurcation analysis, and optimal control in active colloidal and interfacial transport systems.
Keywords
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