Generation of multi-scroll hyperchaotic attractor based on Colpitts oscillator model

Abstract

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.