<![CDATA[Oscillatory instabilities arising from the nonlinear interaction of reaction and transport processes can significantly degrade the performance, stability, and safety of reacting fluid systems. Reduced-order models provide an efficient framework for capturing the essential nonlinear dynamics while enabling systematic bifurcation analysis and optimal control design. A nonlinear reduced-order framework is developed by projecting the governing partial differential equations describing coupled momentum and scalar transport onto a low-dimensional modal basis, resulting in a four-dimensional dynamical system with two velocity modes and two reactive scalar modes. Stability and bifurcation analyses are performed using MATCONT to identify Hopf bifurcation points and limit cycle dynamics. An optimal control problem is subsequently formulated in Pyomo.DAE and solved using IPOPT to minimize oscillatory energy while incorporating a bifurcation-aware constraint that prevents operation near the Hopf boundary. The bifurcation analysis identifies a Hopf bifurcation at a critical Damköhler number, where a complex conjugate pair of eigenvalues crosses the imaginary axis. The optimal control results demonstrate that incorporating the Hopf bifurcation avoidance constraint suppresses oscillatory dynamics, achieving approximately a 90% reduction in the objective function compared with the unconstrained formulation. The proposed reduced-order modeling and control framework provides a low-dimensional, physically motivated representation for investigating oscillatory instabilities in reacting fluid systems. Integrating bifurcation analysis with optimal control provides a computational strategy for maintaining stable operation and suppressing self-sustained oscillations. The present model is intended as a conceptual proof-of-principle framework; validation against full-resolution simulations or experimental reacting-flow data remains an important direction for future work.]]>
