Abstract
The widespread presence of maps in discrete dynamical models needs the usage of efficient algorithms for their investigation. The method of symbolic images is more efficient than exhaustive numerical simulation of trajectories because it transforms a map into a graph through a discretization of the state space, so it opens the way to the usage of graph algorithms and it provides a unified framework for the detection of system features. In this framework, a modification of the algorithm described by Osipenko et al. is proposed and its efficiency is analyzed. Issues on the convergence of the method raise when the dynamical system is described by a not-Lipschitzian nonlinear map in the plane. As case study it is shown the application of the method on an evolutionary model of boundedly rational consumer characterized by the presence of a denominator that can vanish.
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Rotundo, G. (2013). An Investigation of Computational Complexity of the Method of Symbolic Images. In: Proto, A., Squillante, M., Kacprzyk, J. (eds) Advanced Dynamic Modeling of Economic and Social Systems. Studies in Computational Intelligence, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32903-6_9
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DOI: https://doi.org/10.1007/978-3-642-32903-6_9
Publisher Name: Springer, Berlin, Heidelberg
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