In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

中文翻译：

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几类多项式Jerk方程的非混沌行为的确定

在这项工作中，通过使用我们在早期论文中提出的代数准则，我们确定了参数的条件，以保证某些类型的非线性三阶常微分方程的非混沌行为 [公式：见文本] 称为 jerk 方程，其中 [Formula: see text] 是一次多项式 [Formula: see text]。这种方程在文献中经常被用来研究混沌动力学，因为它的形式简单，并且因为它在几个应用问题中作为数学模型出现。因此，确定何时是混沌和非混沌是很重要的。这里陈述的结果是使用上述代数准则证明的，证实并扩展了文献中已经提出的一些结果，为某些混沌方程的非混沌行为提供更简单的证明。我们证明的代数准则是相当普遍的，可以用来研究其他类型常微分方程的非混沌行为。