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INTEGRABILITY AND BIFURCATIONS OF LIMIT CYCLES IN A CUBIC KOLMOGOROV SYSTEM
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| International Journal of Bifurcation and Chaos |
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We investigate the planar cubic Kolmogorov systems with three invariant algebraic curves which have a equilibrium at (1, 1). With the help of computer algebra system MATHEMATICA, we prove that five limit cycles can be bifurcated from a critical point in the first quadrant. Moreover, the necessary conditions of center are obtained, by technical transformation, and its sufficiencies are proved.
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Kolmogorov systems, center-focus problem, Lyapunov constant, limit circle
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