Open AccessGeneration of multi-scroll hyperchaotic attractor based on Colpitts oscillator model
Author(s) -
Bao Bo-Cheng,
Zhong Liu,
Jianzhong Xu,
Linsheng Zhu
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.59.1540
Subject(s) - scroll , colpitts oscillator , phase portrait , attractor , lyapunov exponent , chaotic , control theory (sociology) , bifurcation , bifurcation diagram , topology (electrical circuits) , multistability , piecewise linear function , computer science , mathematics , nonlinear system , physics , mathematical analysis , control (management) , vackář oscillator , telecommunications , archaeology , radio frequency , quantum mechanics , artificial intelligence , combinatorics , local oscillator , history
Based on third-order spiral chaotic Colpitts oscillator model, by introducing two piecewise-linear triangular function, a novel four-dimensional multi-scroll hyperchaotic system is constructed, which can generate 2M+1×2N+1, 2M+1 and 2N+1-scroll chaotic and hyperchaotic attractors. By using phase portrait, Poincaré mapping, Lyapunov exponent spectrum and bifurcation diagram, the dynamical behaviors of the proposed multi-scroll hyperchaotic system are analyzed. These results indicate that Hopf bifurcation point of multi-scroll hyperchaotic system is only related with the control parameter, but its scroll number and ranges of the control parameter for chaotic and hyperchaotic states increase along with the number of turning points. Furthermore, an analog circuit was designed to realize the four-dimensional multi-scroll hyperchaotic system. The results of experimental output and numerical simulation are basically the same.