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This paper initiates a saturated function series approach for chaos generation. The systematic saturated function series methodology developed here can create multiscroll chaotic attractors from a three-dimensional (3D) linear autonomous system with a simple saturated function series controller, including one-directional n-scroll, two-directional n×m-grid scroll, and 3-D n×m×l-grid scroll chaotic attractors. The dynamical behaviors and chaos generation mechanism of multiscroll systems are further investigated by analyzing the system trajectories. In particular, a two-dimensional (2D) Poincare´ return map is rigorously derived for verifying the chaotic behaviors of the double-scroll chaotic attractor, which is a basic generator of various multiscroll chaotic attractors investigated in the paper.