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Displaying similar documents to “Limit cycles of a class of Hilbert's sixteenth problem presented by fractional differential equations.”

Complex Oscillations and Limit Cycles in Autonomous Two-Component Incommensurate Fractional Dynamical Systems

Datsko, Bohdan, Luchko, Yuri (2012)

Mathematica Balkanica New Series

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MSC 2010: 26A33, 34D05, 37C25 In the paper, long-time behavior of solutions of autonomous two-component incommensurate fractional dynamical systems with derivatives in the Caputo sense is investigated. It is shown that both the characteristic times of the systems and the orders of fractional derivatives play an important role for the instability conditions and system dynamics. For these systems, stationary solutions can be unstable for wider range of parameters compared to...

On the number of limit cycles of a generalized Abel equation

Naeem Alkoumi, Pedro J. Torres (2011)

Czechoslovak Mathematical Journal

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New results are proved on the maximum number of isolated T -periodic solutions (limit cycles) of a first order polynomial differential equation with periodic coefficients. The exponents of the polynomial may be negative. The results are compared with the available literature and applied to a class of polynomial systems on the cylinder.