Constructing a chaotic system based on the Silnikov theorem

Based on the Silnikov theorem, a theorem that confirmed the existence of Smale horseshoes sense chaos was set up. Using the theorem, a new kind of quadratic chaotic system could be constructed, which has a unique equilibrium point. A numerical simulation example demonstrated that this system could have chaotic attractor. In particular, the method could be used to generate other quadratic chaotic systems.