Hudson-Rossler model

Fig. 13.19. Relaxation-chaotic oscillations a(t), fe(t), and c(t) for the Hudson-Rossler model.

Two dependent mathematical variables are needed for a network to be capable of periodic behavior. A third is required to permit chaos. It has become quite a sport among the apostles of nonlinear chemical dynamics to invent ever new simple, if not exactly realistic networks that can admit chaos. A classical example, and one of the simplest, is the Hudson-Rossler model [45]. The core of the network is... 

The specific models we will analyse in this section are an isothermal autocatalytic scheme due to Hudson and Rossler (1984), a non-isothermal CSTR in which two exothermic reactions are taking place, and, briefly, an extension of the model of chapter 2, in which autocatalysis and temperature effects contribute together. In the first of these, chaotic behaviour has been designed in much the same way that oscillations were obtained from multiplicity with the heterogeneous catalysis model of 12.5.2. In the second, the analysis is firmly based on the critical Floquet multiplier as described above, and complex periodic and aperiodic responses are observed about a unique (and unstable) stationary state. The third scheme has coexisting multiple stationary states and higher-order periodicities. 

In chapter 12 we discussed a model for a surface-catalysed reaction which displayed multiple stationary states. By adding an extra variable, in the form of a catalyst poison which simply takes place in a reversible but competitive adsorption process, oscillatory behaviour is induced. Hudson and Rossler have used similar principles to suggest a route to designer chaos which might be applicable to families of chemical systems. They took a two-variable scheme which displays a Hopf bifurcation and, thus, a periodic (limit cycle) response. To this is added a third variable whose role is to switch the system between oscillatory and non-oscillatory phases. 

Hudson, J. L. and Rossler, O. E. (1984). Chaos in simple three- and four-variable chemical systems. In Modelling of patterns in space and time, (ed. W. Jager and J. D. Murray). Springer, Berlin. 

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See also in sourсe #XX -- [ ]

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