温州大学学报（自然科学版）
溫州大學學報（自然科學版）
온주대학학보（자연과학판）
JOURNAL OF WENZHOU UNIVERSITY(NATURAL SCIENCES)
2014年
2期
1-7
,共7页
时滞类Lorenz系统%零平衡点%稳定性%Hopf分支
時滯類Lorenz繫統%零平衡點%穩定性%Hopf分支
시체류Lorenz계통%령평형점%은정성%Hopf분지
Delayed Lorenz-like System%Zero Equilibrium Point%Stability%Hopf Bifurcation
对类Lorenz系统的状态变量加上时滞得到一个泛函微分动力系统--时滞类Lorenz系统。首先给出了该系统仅存在零平衡点的条件，然后根据系统在零平衡点处的线性化系统对应的特征方程根的分布情况，给出了系统在零平衡点处稳定性和发生Hopf分支的条件，最后通过一些数值模拟验证了所得结论的正确性。
對類Lorenz繫統的狀態變量加上時滯得到一箇汎函微分動力繫統--時滯類Lorenz繫統。首先給齣瞭該繫統僅存在零平衡點的條件，然後根據繫統在零平衡點處的線性化繫統對應的特徵方程根的分佈情況，給齣瞭繫統在零平衡點處穩定性和髮生Hopf分支的條件，最後通過一些數值模擬驗證瞭所得結論的正確性。
대류Lorenz계통적상태변량가상시체득도일개범함미분동력계통--시체류Lorenz계통。수선급출료해계통부존재령평형점적조건，연후근거계통재령평형점처적선성화계통대응적특정방정근적분포정황，급출료계통재령평형점처은정성화발생Hopf분지적조건，최후통과일사수치모의험증료소득결론적정학성。
The delayed Lorenz-like system proposed in this paper is a system resulting from the addition of time delay to the state variables of Lorenz-like system. Firstly, the condition of Lorenz-like system only at zero equilibrium point was analyzed; secondly, according to the roots distribution of the associated characteristic equation corresponding to the linearized system of the system at the zero equilibrium point, the conditions were obtained for the asymptotic stability of the system and the emergence of Hopf bifurcation when the system stayed at zero equilibrium point;finally, some numerical simulations were given to verify the correctness of the conclusion.
