A simple no-equilibrium chaotic system with only one signum function for generating multidirectional variable hidden attractors and its hardware implementation.

Abstract

This paper proposes a simple no-equilibrium chaotic system with only one signum function as compared with the existing no-equilibrium chaotic ones with at least one quadratic or higher nonlinearity. The system has the offset boosting of three variables through adjusting the corresponding controlled constants. The resulting hidden attractors can be distributed in a 1D line, a 2D lattice, a 3D grid, and even in an arbitrary location of the phase space. Particularly, a hidden chaotic bursting oscillation is also observed in this system, which is an uncommon phenomenon. In addition, complex hidden dynamics is investigated via phase portraits, time series, Kaplan-Yorke dimensions, bifurcation diagrams, Lyapunov exponents, and two-parameter bifurcation diagrams. Then, a very simple hardware circuit without any multiplier is fabricated, and the experimental results are presented to demonstrate theoretical analyses and numerical simulations. Furthermore, the randomness test of the chaotic pseudo-random sequence generated by the system is tested by the National Institute of Standards and Technology test suite. The tested results show that the proposed system has good randomness, thus being suitable for chaos-based applications such as secure communication and image encryption.