Studies on the construction method of a family of multi-scroll chaotic systems

A method for constructing multi-scroll chaotic systems based on shift transformation is presented. Firstly a proper unstable linear system is selected, and the phase space is divided into several parts by a series of parallel interfaces. Then shift transformations of the linear system are implemented so that each space region is dominated by the corresponding new system. Finally the whole system is obtained using a proper nonlinear function based on signum functions. According to this method new multi-scroll chaotic systems with arbitrary odd number scrolls can be constructed, furthermore, some existing chaotic systems can also be modified into multi-scroll systems. Numerical simulations verify the feasibility of the proposed method.