It is unclear to what extent the conditions of Takens' theorem will be met for these discrete-time systems, if ABM are viewed as dynamical systems. Stark et al (2003) provided a version of Takens' theorem for iterated function systems. Mytkowicz et al (2009) view computer systems as dynamical systems, and implement attractor reconstruction accordingly. What is the verdict for discrete-time simulations of ABM, multi-agent systems (MAS) and possibly other complex adaptive systems?
If you can express the ABM as a discrete dynamical system, why not? The main limitation will be the possibly large dimension of the embedding space, since ABMs often consist of a large number of loosely connected complex subsystems.
Hi Michael,
There are some practical issues involved which I can only quote now: 1) the system must be autonomous... in practice this usually boils down to systems that do not have external inputs, 2) the system must be time invariant, 3) the dynamics must be observable from the measurements (on this topic you will find many papers on my RG account).
Thank you very much for your answers. I realized afterwards that I could also have framed my question more specifically in the sense that the attractor reconstruction is meant for the macro-level behaviour of the ABM, which under certain circumstances can have low-dimensional dynamics, e.g. in cases of emergence or self-organization. Generally this situation (ABM) does not have closure in terms of a conventional "state equation" yet I am hoping that by choosing an appropriate observable, an adequate reconstruction of the dynamical phase space may be possible, especially in emergent/SO cases. The cross-fertilization of ABM, dynamical systems and nonlinear time series analysis could have much potential if viable in my humble opinion, but very few have made the connection in the literature from my estimation?
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