Identification of bifurcations and centers in systems with complex dynamic behavior

Abstract

The conclusion from the RHF/4-31G*//RHF/4-31G* structure and frequency calculations is that 1-5 are stable. The structures 2-5 are more rigidly defined than 1, as measured by their lowest (nontorsional) vibrational frequency.The calculated NN bond lengths in 1-5 mimic analogous calculated NN bond lengths in smaller unstrained NH molecules in almost all cases.Assuming the calculated RHF/4-31G*//RHF/4-31G* energy differences accurately represent reality, all five N6 structures are highly metastable to decomposition into three N2 molecules. This

Thermal imaging of breathing patterns during CO oxidation on a Pd/glass cloth

“…The second feature is the nature of the conversion patterns that are of the relaxation–oscillations type; the thermograms in Figure 9 show only the section of the period with high activity. A third feature of these patterns is that the conversion (that is, CO 2 ) oscillations are complex, multipeak (also termed mixed‐mode, for example, Sheintuch and Luss, 1989), and are usually aperiodic in the sense that the details are not reproduced exactly from one period to another. The fourth feature of the observed oscillations is that three time scales are evident in the system: the turnover frequency is less than 1 s in order of magnitude, the period of the relaxation oscillations ranges from 10 to 60 min, while the fast superimposed oscillations have a period of about 1 min.…”

Application of Variable Structure Models to Oscillatory and Spatially-Dependent Processes

“…The model equations are with the parameters a ) 1, b ) -2, c ) 2, d ) -0.8, p ) 5, q ) -6.3, r ) 0.1, λ ) 10, and ) 10 -4 . Models with cubic nonlinearity have long been employed as a simple representation showing complex dynamics in mechanical (Van-der-Pol oscillations) as well as in chemical systems (Sheintuch and Luss, 1989). Analysis of this model can be performed according to section 2.…”