具有两种不同时滞的奇异摄动Riccati微分方程的动力学

Q4 Mathematics
A. El-Sayed, S. Salman, S. Ramadan
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引用次数: 1

摘要

本文研究具有两种不同时滞的Riccati差分方程的奇异摄动问题。首先研究了线性化系统不动点的局部稳定性及其对应的特征方程。其次,我们证明了存在Hopf分岔,其发生条件有限制。然后应用分步法得到离散系统。离散系统的局部稳定性及分岔分析。我们将结果与两种不同时滞的Riccati微分方程的结果进行了比较。最后,通过分岔图、李亚普诺夫指数和相图等数值模拟验证了分析结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the dynamics of the singularly perturbed Riccati differential equation with two different delays
In this paper, we consider the singularly perturbation of the Riccati difference equation with two different delays. At first, we study the local stability of the fixed points and its corresponding characteristic equation of the linearized system. At second, we show that there is Hopf bifurcation with restricted condition for occurrence. Then we get out the discretized system by applying the method of steps. Local stability and bifurcation analysis of the discretized system. We compare the results with the results of the Riccati differential equation with two different delays. Finally, numerical simulations including bifurcation diagram, Lyapunov exponent and phase portraits are carried out to confirm the analytical findings .
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CiteScore
0.30
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