Self-oscillations in implicit singularly perturbed dynamical systems on the plane
Vladimir V. Gotsulenko
National Academy of Sciences of Ukraine Institute of Engineering Thermophysics, 2a Zhelyabov, Kiev, 03680, Ukraine
To implicitly singularly perturbed autonomous systems of ordinary differential equations of second order found some sufficient conditions for the existence of periodic solutions of relaxation (self-oscillation), determined by means of an auxiliary dynamical system that implements a sliding mode. It is shown that so defined periodic motions have typical properties of self-oscillations of relaxation defined autonomous systems of ordinary differential equations with a small parameter at the highest derivative.
implicitly singularly perturbed system, sliding mode, the relaxation periodic solution, self-oscillations.
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MSC: 39A23, 39A33
Vladimir V. Gotsulenko, “Self-oscillations in implicit singularly perturbed dynamical systems on the plane”, Nelin. Dinam., 10:2 (2014), 157–176
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\paper Self-oscillations in implicit singularly perturbed dynamical systems on~the~plane
\jour Nelin. Dinam.
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