CAJ | 학술논문

同宿轨的求解是非线性系统领域的核心问题之一,特别是对动力系统分岔与混沌的研究有重要意义.根据同宿轨的几何特点,采用轨线逼近的方式,通过定义逼近轨线与鞍点的距离,将同宿轨的求解转化为求距离最小值的无约束非线性优化问题.为了提高优化结果的完整性,还提出了基于区间细分的搜索算法和实现方法,并找出了Lorenz系统, Shimizu-Morioka系统和超混沌Lorenz系统等的多个同宿轨道和对应参数,验证了本文方法的有效性.
동숙궤적구해시비선성계통영역적핵심문제지일,특별시대동력계통분차여혼돈적연구유중요의의.근거동숙궤적궤하특점,채용궤선핍근적방식,통과정의핍근궤선여안점적거리,장동숙궤적구해전화위구거리최소치적무약속비선성우화문제.위료제고우화결과적완정성,환제출료기우구간세분적수색산법화실현방법,병조출료Lorenz계통, Shimizu-Morioka계통화초혼돈Lorenz계통등적다개동숙궤도화대응삼수,험증료본문방법적유효성.
@@@@Detecting homoclinic orbits is a key problem in nonlinear dynamical systems, especially in the study of bifurcation and chaos. In this paper, we propose a new method to solve the problem with trajectory optimization. By defining a distance between a saddle point and its near trajectories, the problem becomes a common problem in unconstrained nonlinear optimization to minimize the distance. A subdivision algorithm is also proposed in this paper to improve the integrity of results. By applying the algorithm to the Lorenz system, the Shimizu-Morioka system and the hyperchaotic Lorenz system, we successfully find many homoclinic orbits with the corresponding parameters, which suggests that the method is effective.