Open AccessCubic nonlinear differential system, their periodic solutions and bifurcation analysis
Author(s) -
Saima Akram,
Ahmad Nawaz,
Mariam Rehman
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021655
Subject(s) - maple , mathematics , multiplicity (mathematics) , bifurcation , trigonometric polynomial , homogeneous , symbolic computation , trigonometry , algebraic number , nonlinear system , trigonometric substitution , pure mathematics , bifurcation theory , mathematical analysis , polynomial , combinatorics , physics , bicubic interpolation , linear interpolation , botany , quantum mechanics , biology
In this article, periodic solutions from a fine focus $ U = 0 $, are accomplished for several classes. Some classes have polynomial coefficients, while the remaining classes $ C_{14, 7} $, $ C_{16, 8} $ and $ C_{5, 5}, $ $ C_{6, 6} $ have non-homogeneous and homogenous trigonometric coefficients accordingly. By adopting a systematic procedure of bifurcation that occurs under perturbation of the coefficients, we have succeeded to find the highest known multiplicity $ 10 $ as an upper bound for the class $ C_{9, 4} $, $ C_{11, 3} $ with algebraic and $ C_{5, 5}, $ $ C_{6, 6} $ with trigonometric coefficients. Polynomials of different degrees with various coefficients have been discussed using symbolic computation in Maple 18. All of the results are executed and validated by using past and present theory, and they were found to be novel and authentic in their respective domains.