计算机应用研究
計算機應用研究
계산궤응용연구
APPLICATION RESEARCH OF COMPUTERS
2013年
10期
3038-3040
,共3页
新的混沌系统%同宿轨道%Si'lnikov定理%待定系数法%斯梅尔马蹄
新的混沌繫統%同宿軌道%Si'lnikov定理%待定繫數法%斯梅爾馬蹄
신적혼돈계통%동숙궤도%Si'lnikov정리%대정계수법%사매이마제
new chaotic system%homoclinic orbit%Si'lnikov theorem%undetermined coefficient method%Smale horseshoe
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。
利用Si'lnikov定理構造一箇含有平方項的三維混沌繫統, 且繫統有兩箇平衡點, 有一箇是鞍焦平衡點, 構造的過程錶明該混沌具有Smale馬蹄(同宿軌混沌)。在滿足同宿軌道Si'lnikov定理條件下可以找齣大量的參數值, 使得繫統處于混沌狀態。數值倣真驗證瞭該方法的有效性。最後, 用待定繫數法找到繫統中存在Smale馬蹄, 因而是Si'lnikov意義下的混沌。
이용Si'lnikov정리구조일개함유평방항적삼유혼돈계통, 차계통유량개평형점, 유일개시안초평형점, 구조적과정표명해혼돈구유Smale마제(동숙궤혼돈)。재만족동숙궤도Si'lnikov정리조건하가이조출대량적삼수치, 사득계통처우혼돈상태。수치방진험증료해방법적유효성。최후, 용대정계수법조도계통중존재Smale마제, 인이시Si'lnikov의의하적혼돈。
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 theoretical results. Finally, Smale horseshoses had been found in the system using undetermined-coefficient method, and it was chaotic in the sense of Si'lnikov.
