CAJ | 학술논문

研究了具有双时滞的Mackey‐Glass系统的稳定性与 Hopf分支。从系统线性化方程的特征方程根的分布入手，分别研究了单时滞和双时滞Mackey‐Glass系统的线性稳定性。当系统中的时滞经过一系列临界值时，系统经历了Hopf分支，并且当时滞较大时，系统出现了混沌吸引子。然后，利用中心流形理论和规范型方法分析了分支周期解的稳定性和 Hopf分支的分支方向。最后，数值模拟验证了理论分析结果。
연구료구유쌍시체적Mackey‐Glass계통적은정성여 Hopf분지。종계통선성화방정적특정방정근적분포입수，분별연구료단시체화쌍시체Mackey‐Glass계통적선성은정성。당계통중적시체경과일계렬림계치시，계통경력료Hopf분지，병차당시체교대시，계통출현료혼돈흡인자。연후，이용중심류형이론화규범형방법분석료분지주기해적은정성화 Hopf분지적분지방향。최후，수치모의험증료이론분석결과。
The stability and Hopf bifurcation of Mackey‐Glass system with two time delays are studied . The linear stabilities with one delay and two delays are investigated , respectively . It is found that Hopf bifurcations exist w hen the delays pass through a sequence of critical values , furthermore , the system appears chaotic attractors with large time delays . Then , using the center manifold theorem and the normal form method , the direction and stability of the Hopf bifurcation are determined . In the end , some numerical simulations are carried out for supporting the analytic results .