Abstract
This paper formulates the Chen chaotic system to the extended Kolmogorov system, thereby investigating the physical meaning and energy cycle of Chen system. The Casimir function is introduced to analyze the system dynamics, and its time derivation is chosen to formulate energy cycle. The bound of chaotic attractor is obtained by the Casimir function and Lagrange multiplier. The Casimir function reflects the energy conversion and the distance between the orbit and the equilibria. These relationships are illustrated by numerical simulations.
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