用Si’lnikov定理构造一个新的混沌系统

Constructing new chaotic system based on Si'lnikov theorem

利用Si’lnikov定理构造一个含有平方项的三维混沌系统,且系统有两个平衡点,有一个是鞍焦平衡点,构造的过程表明该混沌具有Smale马蹄(同宿轨混沌)。在满足同宿轨道Si’lnikov定理条件下可以找出大量的参数值,使得系统处于混沌状态。数值仿真验证了该方法的有效性。最后,用待定系数法找到系统中存在Smale马蹄,因而是Si’lnikov意义下的混沌。

Based on the Si＇ lnikov theorem, this paper proposed a new three-dimensional square chaotic system, which had tow equilibrium poits. There was hyperbolic saddle focus. The formation mechanism showed that this chaotic system had Smale horseshoes（homoclinic chaos）. Under satisfying the homoclinic Si＇ lnikov theorem, the large number of parameter values, which could be found, made that the system was chaotic state. Numerical simulation results show the effectiveness of the theo- retical results. Finally, Smale horseshoses had been found in the system using undetermined-coefficient method, and it was chaotic in the sense of Si＇ lnikov.