Open AccessA new piecewise nonlinear chaotic map and its performance
Author(s) -
Xuefeng Zhang,
Jiulun Fan
Publication year - 2010
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.59.2298
Subject(s) - lyapunov exponent , chaotic , logistic map , piecewise , ergodic theory , bifurcation diagram , bifurcation , piecewise linear function , phase space , nonlinear system , mathematics , statistical physics , computer science , mathematical analysis , physics , artificial intelligence , quantum mechanics , thermodynamics
Properties of logistic chaotic map is studied, and it is pointed out that phase space is not ergodic when parameters of the chaotic system change. Based on these analysis, a piecewise logistic chaotic map is constructed. The bifurcation diagram and Lyapunov exponent of logistic and piecewise logistic map are studied, and the properties of randomicity, correlation coefficient and power spectrum etc. of the sequences generated by these two maps are analyzed experimentally. A new performance evaluation index for chaotic system, the bifurcation iteration time, is defined. Simulation results show that the defined piecewise logistic map is not only ergodic in phase space, and its corresponding chaotic performance evaluation indices are also better.