Journal
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
Volume 27, Issue 2, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127417500249
Keywords
Energy function; generalized Hamiltonian realization; Lorenz system; Chen system
Funding
- National Natural Science Foundation of China [61573199, 61403274]
- Application Base and Frontier Technology Research Project of Tianjin of China [13JCQNJC03600]
- South African National Research Foundation Incentive Grants [81705]
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Solving the linear first-order Partial Differential Equations (PDEs) derived from the unified Lorenz system, it is found that there is a unified Hamiltonian (energy function) for the Lorenz and Chen systems, and the unified energy function shows a hyperboloid of one sheet for the Lorenz system and an ellipsoidal surface for the Chen system in three-dimensional phase space, which can be used to explain that the Lorenz system is not equivalent to the Chen system. Using the unified energy function, we obtain two generalized Hamiltonian realizations of these two chaotic systems, respectively. Moreover, the energy function and generalized Hamiltonian realization of the Lu system and a four-dimensional hyperchaotic Lorenz-type system are also discussed.
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