Simplest chaotic system with a hyperbolic sine and its applications in DCSK scheme

This work describes the simplest chaotic system with a hyperbolic sine non‐linearity, accompanied by analysis of Lyapunov exponents, bifurcations, and stability. The corresponding simple chaotic circuit using only diodes and linear components is designed and implemented. Finally, an application of the system to spread spectrum communication based on differential chaos shift keying (DCSK) is presented. Since the hyperbolic sine is an odd function of its argument, the system is antisymmetric and exhibits symmetry breaking where the attractors split or merge as some bifurcation parameter is changed. The proposed system is especially simple both from the structure of the equations and in its electronic circuit realisation. Compared with the traditional DCSK scheme of a Chebyshev sequence, the system can reduce the bit error rate in the presence of noise.