Abstract
The problem of oscillations detection for nonlinear systems is addressed. The notion of homogeneity in bi-limit from (Andrieu, et al., 2008) is extended to local homogeneity. Next, sufficient conditions of oscillations existence for locally homogeneous systems are formulated. The proposed approach allows one to estimate the number of limit cycles and the regions of their location. Efficiency of the technique is demonstrated on two academic examples.
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