Generating New Chaos with a Switching Piecewise-Linear Controller

Abstract

In this paper, we study the problem of generating chaotic attractors by using a switching type of piecewise linear controller. A new chaotic system is generated by designing a switching piecewise-linear controller . Some basic dynamical properties, such as Lyapunov exponents, fractal dimension, equilibrium and chaotic dynamical behaviors of the new chaotic system are studied. Furthermore, dynamical structures also have been discussed by parameters and controller variation, either numerically or analytically. Of particular interest is the fact that chaotic system can generate two opposite direction attractors in a wide parameter range. According to its geometric locations, two attractors are called upper-attractor and lower-attractor. The obtained results show clearly that the system discussed in this paper is a new chaotic system and deserves further detailed investigation.