Open AccessConstruction of grid multi-scroll chaotic attractors and its circuit implementation with polynomial and step function
Author(s) -
Chen Shi-bi,
Yicheng Zeng,
Xu Mao-Lin,
Chen Jia-Sheng
Publication year - 2011
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.60.020507
Subject(s) - scroll , attractor , chaotic , polynomial , phase space , topology (electrical circuits) , saddle , function (biology) , computer science , mathematics , algorithm , mathematical analysis , physics , mathematical optimization , artificial intelligence , combinatorics , archaeology , evolutionary biology , biology , history , thermodynamics
A constructing approach to generating N×M-scroll attractors with polynomial and step function is reported. In Chuas circuit, only two or three scrolls can be generated by traditional polynomial function. On this basis, the multi-scroll of x direction in phase space is obtained by polynomial shift. And then the saddle-focus equilibrium points with index-2 in phase space are extended by combining both polynomial and step function, which makes it possible to extend the multi-scroll in y direction. Then the grid multi-scroll chaotic attractors are generated. The main feature of this constructing approach is generating grid multi-scroll chaotic attractors by combining both smooth curves and non-smooth curves for the first time. And the arbitrary planar grid multi-scroll chaotic attractors array can be generated by adjusting the values of natural numbers N and M. The effectiveness of this method has been verified by theoretical analysis, numerical simulation and circuit simulation.