This work presents a comprehensive analysis of nonlinear dynamics in a discrete-time chlorine dioxide-iodine-malonic acid (CDIMA) reaction model, combining theoretical bifurcation analysis with numerical validation. Using forward Euler discretization and normal form theory, we establish the existence of codimension-two bifurcations at the system's positive fixed point, characterized by 1:2, 1:3, and 1:4 strong resonances. Numerical simulations quantitatively confirm these theoretical predictions, revealing three distinct dynamical regimes: (1) stable period-2 limit cycles emerging from 1:2 resonance, demonstrating rhythmic bistable oscillations; (2) complex period-3 orbits arising from 1:3 resonance, indicating tripled-state nonlinear interactions; and (3) a mixed periodic-chaotic regime generated by 1:4 resonance, exhibiting sensitive dependence on initial conditions. The remarkable agreement between analytical and computational results provides robust verification of the CDIMA system's rich dynamical repertoire. These findings offer new insights into chemical oscillator control, with potential applications ranging from engineered reaction-diffusion systems to biological rhythm regulation. The integrated theoretical-numerical approach developed here establishes a general framework for investigating complex behaviors in nonlinear chemical systems.