Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

Autor(es)

Messias, Marcelo ^[1] ; Silva, Rafael Paulino ^[2]

Afiliação do(s) autor(es)

^[1] FCT UNESP, Fac Ciencias & Tecnol, Dept Matemat & Comp, BR-19060900 Presidente Prudente, SP - Brazil

^[2] IBILCE UNESP, Inst Biocincias Letras & Cincias Exatas, Dept Matemat, BR-15054000 Sao Jose Do Rio Preto, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 30, n. 8 JUN 30 2020.
• Citações Web of Science: 0

Resumo

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 (x) triple over dot = j(x, (x)over dot, (x)double over dot), called jerk equations, where j is a polynomial of degree n. 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. (AU)

• Processo FAPESP: 19/10269-3 - Teorias ergódica e qualitativa dos sistemas dinâmicos II
• Beneficiário: Claudio Aguinaldo Buzzi
• Modalidade de apoio: Auxílio à Pesquisa - Temático