To date there are three basic system theories, and one process theory.
Systems can be described as:
Process are described by bios theory, developed by Hector Sabelli.
If an economy is a system, then any one of the systems theories may be the most accurate model for how to understand how an economy works. But if an economy is a process, then bios theory will provide the most accurate model (of all the models we have available).
I will note this: the order of complexity goes, from least to most: equilibrium, cycles, chaos, bios.
If an economy is a simple system, it can be described using equilibrium. If it is a complex system, it can be described with chaos (and, of course, if it is somewhere in between, it can be described with cycles). And we see all three being used. It is possible for each to provide some useful information about an economy precisely because, even if an economy is a process, it will contain within it chaos, cycles, and equilibria as less complex constiuent parts. Thus, an equilibrium theory can tell us something about an economy, even if it may be a special case, or an attempt to remove time from the equation to allow us to understand what is happening in a given moment. But that is in fact all an equilibrium theory can do. A cycle theory is more complex, and can explain more things. We can get things ranging from Austrian Business Cycle Theory (which is really a theory which explains why the economy sometimes is simpler than it should be, and thus acts accordingly) to Schumpeter's creative destruction theory of entrepreneurship (insufficient, to be sure, but a great improvement on equilibrium theories, and moving in the right direction, toward process). A chaos theory is more complex yet -- we get the introduction of such concepts as self-organization, strange attractors, and dissipative structures (where you have to have change to maintain the structure, meaning that the more things change, the more they stay the same). Yet each of these do not allow for creativity. Nothing new is made -- the system is merely maintained. With equilibrium, it is maintained at a stable point; with cycles it is maintained at and between two stable points; with chaos, you have the entire phase space investigated, but once it is investigated, you reach a steady-state. Do any of these sound like an actual economy?
Bios theory describes processes which are in fact creative. In mathematical terms, a new phase space is created. Thus, bios can appear to be chaotic -- and will indeed have chaos as its immediate foundation (with cycles, and equilibrium as even deeper foundations), including self-organization -- but rather than simply filling the given phase space, a biotic process creates a new phase space, which it can then investigate.
Sabelli identifies the following as essential features of creative processes:
1) diversification -- "variety increases with time" (20)
2) complexification -- that is, it must be heterogeneous
3) novelty -- "non-repetitive change" (21) which is "beyond chance" (22)
4) episodic patterning -- that is, new patterns of limited lifetime (complexes) are generated (22)
5) autogenesis/autodynamic -- "Every change brings on the enxt one, so there is a correlation between steps (autocorrelation)" (22)
6) irreversibility /asymmetry -- that is, time matters
8) aperiodic patterning -- power law distribution, and highly sensitive to inputs (23)
9) non-stationarity -- "creative biotic processes have a global sensitivity to initial conditions absent in chaotic attractors" that cause the system to jump into a new phase space (83-4).
Such biotic processes are "generated by action, conservation, and bipolar feedback" (8). To have any kind of physical process, you have to have action, matter, and information. To have a biotic process, the information you need is bipolar feedback. All of these should sound familiar to Austrian economists. Sabelli points out too that bios creates levels of complexity such that "Simple processes have priority, and complex processes have supremacy" (8). In other words mathematical processes have priority, and physical processes have supremacy; physical processes have priority, and chemical processes have supremacy; chemical processes have priority, and biological processes have supremacy; biological processes have priority, and psychological processes have supremacy; psychological processes have priority, and social processes (such as economies) have supremacy (Sabelli reverses these two, but it makes little sense to think that a social process can exist prior to its constituent parts -- humans). The parts create the processes, and "In turn, complex processes feedback into their simple environments and control it through their greater informational content" (8). This is one kind of bipolar feedback -- self-organization creating the process, and the process influencing those interactions. In economic terms, though, "Bipolar feedback includes cooperation and competition as well as abundance and scarcity" (10), and supply and demand (567).
Indeed, what kind of economy does bios theory describe? What kinds of economies to the systems theories describe? What would one expect to happen if you based your economic policies on each of the systems theories described? What would one expect if one based them on process theory?