Numerical study of limit cycles for two perturbed integrable non-Hamiltonian systems

Bifurcation of limit cycles for two perturbed integrable non-Hamiltonian systems is investigated by using both qualitative analysis and numerical exploration. The investigation is based on detection functions which are particularly effective for the integrable non-Hamiltonian systems with perturbed terms. The study reveals that the perturbed non-Hamiltonian system (6) has only 3 limit cycles, whereas the perturbed integrable non-Hamiltonian system (7) has 4 limit cycles. By using method of numerical simulation, the distributed orderliness of these limit cycles is observed, and their nicety places are determined. The study also indicates that each of these limit cycles passes the corresponding nicety point.