Dynamical systems and reaction kinetics networks

This thesis investigates the interaction between dynamical systems theory and chemical reaction kinetics. Focusing on the Brusselator and Lengyel–Epstein models, it analyzes the conditionsunderwhichthesesystemstransitionfromstableequilibriatoperiodicoscillations (via Hopf bifurcation) and spatial patterns (via Turing bifurcation). The stability of the systems is first studied in the context of ordinary differential equations (ODEs), followed by the inclusion of diffusion to formulate reaction-diffusion systems. Linear stability analysis using Jacobian matrices and eigenvalues is employed to identify bifurcation thresholds, and numerical simulations are conducted to visualize pattern formation. The primary goal is to provide theoretical and computational insights into the mechanisms underlying complex behaviorsobservedinchemistryandbiology,andtodemonstratehowsuchbehaviorsemerge underspecific parametricconditions.