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Bifurcation of limit cycles for two integrable non-Hamiltonian systems with perturbed terms

Bifurcation of limit cycles for two integrable non-Hamiltonian systems with perturbed terms is investigated using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the perturbed integrable non-Hamiltonian systems. The study reveals that each of the two systems has 8 limit cycles using detection function approach. By using method of numerical simulation, the distributed orderliness of the 8 limit cycles is observed and their nicety places are determined. The study also indicates that each of the 8 limit cycles passes the corresponding nicety point. The results presented here are helpful for further investigating the Hilbert's 16th problem.