The Related Extension and Application of the Ši'lnikov Theorem | Zendy

Baoying Chen | Zendy

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The Related Extension and Application of the Ši'lnikov Theorem

Author(s) -

Baoying Chen

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/287123

Subject(s) - homoclinic orbit , extension (predicate logic) , mathematics , chaotic , set (abstract data type) , quadratic equation , pure mathematics , discrete mathematics , computer science , bifurcation , artificial intelligence , physics , geometry , quantum mechanics , nonlinear system , programming language

The traditional Ši'lnikov theorems provide analytic criteria for proving the existence of chaos in high-dimensional autonomous systems. We have established one extended version of the Ši'lnikov homoclinic theorem and have given a set of sufficient conditions under which the system generates chaos in the sense of Smale horseshoes. In this paper, the extension questions of the Ši'lnikov homoclinic theorem and its applications are still discussed. We establish another extended version of the Ši'lnikov homoclinic theorem. In addition, we construct a new three-dimensional chaotic system which meets all the conditions in this extended Ši'lnikov homoclinic theorem. Finally, we list all well-known three-dimensional autonomous quadratic chaotic systems and classify them in the light of the Ši'lnikov theorems

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