Hmm, from what I have read of chaos theory which is probably not enough, a system may start off as random but quickly becomes bifurcated into two "strange attractors", and then continues on into a chaotic state (which may display considerable order). I have therefore often thought as a biologist that the wet-dry cycles of wetlands, especially those associated with rivers, were bifurcated in such a way.
The Murray is so highly disturbed as to be almost unrecognisable but nevertheless the wet-dry cycles of associated wetlands still occurs (somewhat). In fact I watched as the salt lakes near me went from brimming during the 2011 flood to now when they are battling to contain water, however they are now completely disconnected from the river which has no floodplain whatsoever where I am, as it is all levied. However in less saline lakes the fauna also cycle with flood and drought, so there are suites (guilds?) of fauna that are prevalent when it is wet, and others that predominate when it is dry. It would be no surprise to me if the Murray was found to be bifurcated, then the regime and its wetlands would be in harmony. Nevertheless either rivers or wetlands could independently have more than one stable state, but if connected by ephemeral inundation this seems unlikely.
Thus you may have probably found an example of chaos theory, and it may help to set the mathematicians onto it. I gather without reading your paper so far, that it is the very ability of the streams to achieve these different states that confers the resilience (?). This would I imagine assist rivers during the ENSO cycles since there would not be much point in returning to a flood-type drainage paradigm in a trending El Nino and vice-versa with La Nina.
Thus the whole wet-dry, bifurcated state systems may be in response to climate cycles ultimately. After all Australia has had ephemeral lakes and rivers since the breakup of Gondwana so the ability of the system to withstand changes and recover and the way in which it does this, i.e. through bifurcation, is going to be quite well established!
However the ability of an ecosystem to withstand perturbations and recover and thus be resilient depends on it being a steady state, which depends on successional stage and extent of disturbance. Thus an early successional stage such as highly disturbed system e.g. logged forest, will have limited resilience to impacts such as fire. However a complex undamaged one will limit damage and recover rapidly. Studies in Australia have shown that intact forested catchments hold more water than logged ones, and studies such as Hubbard Brook have shown that when forests are logged not only moisture but nutrients get lost in massive amounts. In my studies on soils recently it also appears the same thing applies to soil carbon.
Thus fundamentally the Murray is stuffed, even if you could find some skeleton of its bifurcated nature, and will not do well given extremes of drought etc. due to its disturbance levels. However the few intact streams with intact riparian vegetation and relatively undisturbed catchments that can be found may very well have excellent responses, as they will be resilient.
It would be very important in any studies to characterise the degree of disturbance, especially to make comparisons between catchment behavior.
Otherwise your results could be confounded by level of disturbance. That is, a disturbed catchment, even involving just roading, may show a poorer degree of resilience and have a more non-equilibrium nature, hence its responses may be not consistent and even in quite disturbed (e.g. logged) catchments be all over the place in response to disturbances. So you may find one result one year and the next the next, thinking this is normal, but if the system were intact instead of damaged you may get more of a steady state. Alternatively if you studied an intact stream ecosystem you may find it has more consistent responses. So establishing whether a system is bifurcated or not may not be as straightforward as it looks.
Food for thought, without having yet read your paper so you may have already accounted for all of this!