Cubic nonlinear differential system, their periodic solutions and bifurcation analysis
Copyright policy )Cubic nonlinear differential system, their periodic solutions and bifurcation analysis
<abstract><p>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.</p></abstract>
- Government College University, Faisalabad Pakistan
- Bahauddin Zakariya University Pakistan
focal values, bifurcation method, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, algebraic and trigonometric coefficients, periodic solutions, Positive solutions to nonlinear boundary value problems for ordinary differential equations, limit cycle, QA1-939, Linear boundary value problems for ordinary differential equations, multiplicity, Periodic solutions to ordinary differential equations, Mathematics, Bifurcation theory of functional-differential equations
focal values, bifurcation method, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, algebraic and trigonometric coefficients, periodic solutions, Positive solutions to nonlinear boundary value problems for ordinary differential equations, limit cycle, QA1-939, Linear boundary value problems for ordinary differential equations, multiplicity, Periodic solutions to ordinary differential equations, Mathematics, Bifurcation theory of functional-differential equations
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