Hidden oscillation and chaotic sea in a novel 3d chaotic system with exponential function

In this work, a novel 3D chaotic system which has an exponential function is proposed. Especially, the sum of Lyapunov exponents in the proposed system is 0. It indicates that the system can generate attractive sea not attractor. In comparison with some other 3D chaotic systems, this type of chaotic system is relatively rare. In particular, the proposed system has non-equilibrium point, and it can produce hidden sea. Furthermore, the perpetual point of the proposed system is calculated. It is considered to be potentially related to the generation of hidden dynamics. By using the dynamic analysis tool such as 0-1 test and 2D dynamical map, the dynamic behaviors with different control parameters are analyzed. And then, based on the proposed 3D chaotic system, two new system models are reconstructed. The new model can produce the rotational hidden attractive sea with different angles. DSP implementation shows the feasibility of the system for industrial applications.

Automated summary

In this paper, a novel 3D chaotic system with an exponential function is proposed, which can generate an attractive sea. The proposed system is relatively rare compared to other 3D chaotic systems and has a non-equilibrium point. The feasibility of the system for industrial applications is shown through DSP implementation.