Constructing 3D conservative chaotic system with dissipative term based on Shilnikov theorem

Given the uniform structure observed in existing conservative chaotic systems, this paper presents a novel approach for constructing 3D conservative chaotic systems with dissipative terms, utilizing the Shilnikov theorem. To demonstrate the effectiveness of the proposed method, an example system is presented. The researches show that the dissipative term and angular frequency have important influence on the motion of system. Remarkably, this system exhibits distinct forms of conservative chaos and invariant torus. Additionally, we further propose a derivative system of the example system to expand its range of motion. Numerical analysis reveals an intriguing coexistence phenomenon in the system, which will be visually demonstrated using phase diagrams and basins of attraction in the paper. Finally, the analog circuits for both systems are designed, yielding results that closely matched the numerical simulations.