Analysis and application of a 3D chaotic system with an extremely extensive range of amplitudes and offset boosting

Abstract The study of high-dimensional chaotic systems has been the subject of considerable research interest, whereas the complex characteristics of low-dimensional chaotic systems have been largely overlooked. A new 3 dimensional (3D) chaotic system containing only two kinds of nonlinear terms is constructed based on the Lorenz system to enrich the theory of chaotic systems and improve the complex properties of low-dimensional chaotic systems. The system lacks a symmetric structure; however, under the influence of the symmetric parameter α , the system attains a symmetric state and can produce attractors with a symmetric structure. Under the parameter β , the system can realize the regulation of amplitude, frequency, and nonlinear offset boosting of three signals simultaneously. The parameter γ can realize the control of two signal amplitude and frequency at the same time. The system always remains chaotic when the parameters β and γ are varied in a great range. In addition, this 3D chaotic system has offset boosting behavior in arbitrary single and multiple directions, and the offset constant has a wide range of values. These features provide great convenience for secure communications and weak signal engineering applications. Further, analog circuit simulations and DSP (Digital Signal Processor) hardware circuits confirm the parametric modulation of the system and the offset boosting behavior in any direction. Moreover, taking advantage of the extensive offset range, a synchronization controller is designed for the drive and response systems. Finally, the modulation of offsets with a wide range of values realizes the encrypted transmission of binary digital information and lays the foundation for future engineering applications.