TY - JOUR
T1 - A gallery of Lorenz-like and Chen-like attractors
AU - Wang, Xiong
AU - Chen, Guanrong
PY - 2013/4
Y1 - 2013/4
N2 - In this article, three-dimensional autonomous chaotic systems with two quadratic terms, similar to the Lorenz system in their algebraic forms, are studied. An attractor with two clearly distinguishable scrolls similar to the Lorenz attractor is referred to as a Lorenz-like attractor, while an attractor with more intertwine between the two scrolls similar to the Chen attractor is referred to as a Chen-like attractor. A gallery of Lorenz-like attractors and Chen-like attractors are presented. For several different families of such systems, through tuning only one real parameter gradually, each of them can generate a spectrum of chaotic attractors continuously changing from a Lorenz-like attractor to a Chen-like attractor. Some intrinsic relationships between the Lorenz system and the Chen system are revealed and discussed. Some common patterns of the Lorenz-like and Chen-like attractors are found and analyzed, which suggest that the instability of the two saddle-foci of such a system somehow determines the shape of its chaotic attractor. These interesting observations on the general dynamic patterns hopefully could shed some light for a better understanding of the intrinsic relationships between the algebraic structures and the geometric attractors of these kinds of chaotic systems. © 2013 World Scientific Publishing Company.
AB - In this article, three-dimensional autonomous chaotic systems with two quadratic terms, similar to the Lorenz system in their algebraic forms, are studied. An attractor with two clearly distinguishable scrolls similar to the Lorenz attractor is referred to as a Lorenz-like attractor, while an attractor with more intertwine between the two scrolls similar to the Chen attractor is referred to as a Chen-like attractor. A gallery of Lorenz-like attractors and Chen-like attractors are presented. For several different families of such systems, through tuning only one real parameter gradually, each of them can generate a spectrum of chaotic attractors continuously changing from a Lorenz-like attractor to a Chen-like attractor. Some intrinsic relationships between the Lorenz system and the Chen system are revealed and discussed. Some common patterns of the Lorenz-like and Chen-like attractors are found and analyzed, which suggest that the instability of the two saddle-foci of such a system somehow determines the shape of its chaotic attractor. These interesting observations on the general dynamic patterns hopefully could shed some light for a better understanding of the intrinsic relationships between the algebraic structures and the geometric attractors of these kinds of chaotic systems. © 2013 World Scientific Publishing Company.
KW - Chaotic attractor
KW - Chen system
KW - Generalized Lorenz canonical form
KW - Lorenz system
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-84877951071&origin=recordpage
U2 - 10.1142/S0218127413300115
DO - 10.1142/S0218127413300115
M3 - RGC 21 - Publication in refereed journal
VL - 23
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
SN - 0218-1274
IS - 4
M1 - 1330011
ER -