An investigation of computational complexity of the method of symbolic images

The widespread presence of maps in discrete dynamical mo,dels needs the usage of efficient algorithms for their investigagtion. The method of symbolic images is more efficient that 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 deascribed by Osipenko et al. is proposed and its efficiency is analysed Issues on the convergence of the method raise when the dynamical system is described by a not-Lischitzian nonlinear map in the plane. As case study it is sbhown the application of the method on an evolutionary model of boundedly rational consumer characterized by the presence of a denominator that can vanish.