论文标题
两个耦合的一阶频率的系统与二级多项式右侧
Solution of the system of two coupled first-order ODEs with second-degree polynomial right-hand sides
论文作者
论文摘要
初始值问题的显式解决方案显示了2个耦合的一阶颂歌的自主系统的子类，其二级多项式右侧，因此具有12个先前的任意（时间不依赖时间）系数。如果12个系数通过10个以前的任意参数表示，则可以明确提供解决方案；还可以明确解决以12个系数表达这10个参数的逆问题，但发现这意味着12个系数必须满足4个代数的约束，这是一个明确表现出的4个代数约束，该案例还完全限制了一般的限制性。确定特别有趣的模型。
The explicit solution of the initial-values problem is exhibited of a subclass of the autonomous system of 2 coupled first-order ODE s with second-degree polynomial right-hand sides, hence featuring 12 a prior arbitrary (time-independent) coefficients. The solution is explicitly provided if the 12 coefficients are expressed by explicitly provided formulas in terms of 10 a prior arbitrary parameters; the inverse problem to express these 10 parameters in terms of the 12 coefficients is also explicitly solved, but it is found to imply as it were, a posterior that the 12 coefficients must then satisfy 4 algebraic constraints, which are explicitly exhibited.Special sub cases are also identified the general solutions of which are completely periodic with a period independent of the initial data, or are characterized by additional restrictions on the coefficients which identify particularly interesting models.
