Mixed-mode oscillations and chaos in a complex chemical reaction network involving heterogeneous catalysis.

This article investigates the nonlinear dynamical behavior of a complex isothermal reaction network involving heterogeneous catalysis, modeled by a system of ordinary differential equations derived from a catalytic surface reaction scheme with seven state variables and thirteen parameters. Using the Chemical Reaction Network Toolbox (CRNT), the network is shown to admit multiple steady states, and bifurcation continuation analysis via MatCont reveals various bifurcations, including limit point, Bogdanov–Takens, generalized Hopf, period doubling (PD), and generalized period doubling (GPD). Numerical simulations around PD and GPD bifurcations demonstrate rich nonlinear phenomena such as simple sustained oscillations, mixed-mode oscillations (MMOs), MMO-type chaos, and non-MMO-type chaos, with period-doubling and period-adding routes to chaos identified. The study also highlights that maximum Lyapunov exponents, commonly used to detect chaos, can be positive for some non-chaotic orbits in this system, questioning their reliability as a sole indicator of chaos. These findings contribute rare examples of MMOs and MMO-type chaos in heterogeneous catalysis systems that are neither homogeneous nor electrochemical, emphasizing that nonlinear dynamics arise from the network's structural complexity rather than thermal effects or autocatalytic reactions.