Two different distributions of limit cycles in a quintic system

Volume 8, Issue 3, pp 255--266 http://dx.doi.org/10.22436/jnsa.008.03.10

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Authors

Hongwei Li - School of Science, Linyi University, Linyi, 276005, China. Yinlai Jin - School of Science, Linyi University, Linyi, 276005, China.

Abstract

In this paper, the conditions for bifurcations of limit cycles from a third-order nilpotent critical point in a class of quintic systems are investigated. Treaty the system coefficients as parameters, we obtain explicit expressions for the first fourteen quasi Lyapunov constants. As a result, fourteen or fifteen small amplitude limit cycles with different distributions could be created from the third-order nilpotent critical point by two different perturbations.

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Keywords

• Third-order nilpotent critical point
• center-focus problem
• bifurcation of limit cycles
• quasi-Lyapunov constant.

MSC

•  34C05
•  34C07

References

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