Employing the Differential Dynamics Method, a nonlinear dynamic model is set up to describe the international financial crises contagion within a short time between two countries. The two countries’ control force depending on the timely financial assistance, the positive attitude and actions to rescue other infected countries, and investor confidence aggregation, and the immunity ability of the infected country are considered as the major reasons to drive the nonlinear fluctuations of the stock return rates in both countries during the crisis. According to the Ordinary Differential Equations Qualitative Theory, we found that there are three cases of financial crises contagion within a brief time between two countries: weak contagion with instability but inhibition, contagion with limit and controllable oscillation, and strong contagion without control in a brief time.
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