有时间延迟的市场模型中的同步问题

Ghassan Dibeh, Omar El Deeb
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引用次数: 0

摘要

我们研究了一个由 N=2 个耦合非线性延迟微分方程组成的系统,该系统代表了金融市场的动态。在这种时延系统中,耦合振荡已经被推导出来。我们对小时间延迟系统进行线性化,并研究其集体动力学。通过分析和数值求解,我们得到了分岔图,并分析了与系统频率类参数和时间延迟相关的振幅死亡、相位锁定、极限循环和市场同步等相应区域。我们进一步用数值方法探讨了 N>2 的高阶系统,并证明在适当参数化的情况下,N-资产耦合模型可以保持极限循环。
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Synchronization in a market model with time delays
We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N-asset models with appropriate parameterization.
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