Numerical study of isothermal heterogeneous catalysis exhibiting multiple steady states, limit cycles, and chaos in a complex reaction network

Abstract

AbstractWe analyze the nonlinear dynamics of an isothermal system involving complex heterogeneous catalytic reactions by numerical simulation. Multiple steady states, limit cycles, torus, and chaos are found, which demonstrate that these nonlinear behaviors are derived from the intricacy of chemistry itself, instead of either thermal or autocatalytic effects. The steady‐state multiplicity is determined by the chemical reaction network toolbox. Starting from one of the steady states, bifurcations are detected via the variation of the system parameters using numerical continuation software. Bifurcations, such as limit points, cusp bifurcations, Hopf bifurcations, zero Hopf bifurcations, limit cycles, and torus are found. Numerical simulations show two routes of transition to chaos due to torus breakdown. One route is due to the loss of torus smoothness. The other is via period‐doubling bifurcations of the limit cycles. Lyapunov exponents are calculated, and positive values are obtained for the chaotic dynamics. Poincare maps and power spectrum densities are also shown to determine the chaotic orbits.