Journal
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
Volume 45, Issue 3, Pages 1597-1611Publisher
WILEY
DOI: 10.1002/mma.7876
Keywords
analytic first integrals; Darboux first integrals; exponential factors; invariant algebraic surfaces; 3D Van der Pol-Duffing system
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The integrability of the three-dimensional Van der Pol-Duffing system was studied, revealing that under certain conditions the system has no analytic and Darboux first integrals at the neighborhood of the origin. The stability and instability of the singular points were used to investigate the C-1 integrability of this type of system.
In this work, we focus on studying the integrability of the following three-dimensional Van der Pol-Duffing system (x) over dot =-m(x(3) - mu x - y), (y) over dot = x - y - z, (z) over dot = beta y. More precisely, if m beta not equal 0, then the above system has no analytic and nor Darboux first integrals at the neighborhood of the origin. Also, the stability and instability of the singular points are employed to investigate the C-1 integrability of this type of system.
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