Design of a New 3D Chaotic System Producing Infinitely Many Coexisting Attractors and Its Application to Weak Signal Detection

Abstract

This paper proposes a new 3D chaotic system, which can produce infinitely many coexisting attractors. By introducing a boosted control of cosine function to an original chaotic system, as the initial conditions periodically change, the proposed chaotic system can spontaneously output infinitely many chaotic sequences of different amplitudes in two directions in the phase plane. This means that the proposed system can output more key information as a pseudo-random signal generator (PRSG). This is of great significance in the research of weak signal detection. In comparison with the original chaotic system, the chaotic behavior of the proposed system is obviously enhanced due to the introduction of the boosted control function. Then, by adding the mathematical models of a weak signal and a noise signal to the proposed chaotic system, a new chaotic oscillator, which is sensitive to the weak signal, can be restructured. With the change of weak signal amplitude and angular frequency, the dynamical state of the detection system will generate a big difference, which indicates that the weak signal can be detected successfully. Finally, the proposed chaotic system model is physically realized by DSP (Digital Signal Processing), which shows its feasibility in industrial implementation. Especially, since a third-order chaotic system is the lowest-dimensional continuous system that can generate infinitely many coexisting attractors, the proposed chaotic system is of great value in the basic research of chaos.