Abstract
In this paper, we explore the rich dynamics in the Chen system using Runge–Kutta method and Deep Neural Networks (DNNs). Compared with the Lorenz system, we find that the first return map [Formula: see text] of the Chen system exhibits a more complex structure of continuous regions in the Poincaré section. Moreover, the existence of six crossing blocks with respect to the second return map implies that there is a closed invariant set [Formula: see text] in the Poincaré section such that [Formula: see text] is semi-conjugate to a 6-shift map, thus demonstrating remarkably chaos in the Chen system.
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