Homoclinical chaos and the period-adding route to complex non-chaotic attractors in fluidized bed catalytic reactors

Non-chaotic, complex attractors with high periodicities formed through the third kind of period-adding (A.V. Holden, Fan Yin-Shui, Chaos, Solitons & Fractals 2 (1992) 221–236) have been uncovered for bubbling fluidized bed catalytic reactor. A scenario of transition from soft oscillations to hard oscillations characterised by bursting takes place via a very thin strip of homoclinic chaos which fulfills Šilʹnikovʹs condition. Diagrams with staircase structures for the periodic orbits undergoing period-adding bifurcation sequence Pn → Pn+1 were constructed and compared with other cases of period-doubling bifurcation. The differences between the characteristics of period and peak bifurcation have been elucidated. For this relatively new period-adding bifurcation mechanism, a new quantitative relation between the magnitude of the period and the number of the periods has been discovered and discussed.