PARALLEL GLOBAL-ANALYSIS METHOD FOR NONLINEAR SYSTEMS BASED ON CELL MAPPING

The response characteristic of a nonlinear dynamical system is primarily determined by its intrinsic global structure. Conducting global characteristic analysis can delineate the morphological features of the system's global structure, thereby providing a comprehensive understanding of the system's multiple stable attractors and the morphology of their basins of attraction. Currently, the cell mapping method, based on the idea of state space discretization, has become the most effective approach for characterizing the global structures of nonlinear dynamical systems. Firstly, a parallel-reconstruction algorithm rooted in cell-mapping theory is first introduced to refine the cell-to-cell mapping and cell-classification procedures, thereby markedly accelerating the numerical integration that dominates global analysis. Subsequently, by exploiting high-dynamic-range memory hierarchies and large-scale parallel computing, a computationally efficient yet rigorously accurate parallel global-analysis method for cell-mapping processes is established. Finally, the proposed parallel global-analysis method is applied to delineate the global structure of a two-dimensional Mathieu–Duffing oscillator and a three-dimensional Lorenz system. Meanwhile, for the Lorenz system discretized into a 51 × 51 × 61 state-space grid, the total execution time is reduced by 81 % and 83 % relative to classical cell-mapping when 10 and 100 parallel cell units are employed, respectively, which verifies the accuracy and feasibility of the proposed parallel global-analysis method for nonlinear systems.