The work is devoted to the development of efficient parallel algorithms for the computation of large-scale basins of attraction. Since the required computational resources increase exponentially with the dimension of a dynamical system, it is common to get into memory saturation or in a secular elaboration time.

This paper presents a code, based on a cell mapping method, that evaluates basins of attraction for high-dimensional systems by exploiting the parallel programming. The proposed approach, by using a double-step algorithm, permits, i) to fully determine the basins in all the dimensions ii) to evaluate 2D Poincaré sections of the system. The code is described in all its parts: the shell, in charge of the core management, permits to split over a multi-core environment the computing domain, it carries out an efficient use of the memory.

A preliminary analysis of the performances is undertaken also by considering different dimensional grids; the optimal balance between computing cores and memory management cores is studied.

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