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Generally speaking, a piecewise smooth system can bifurcate more limit cycles than a smooth one.
In this section, two perturbation methods are given in order to obtain more limit cycles.
Our results show that a piecewise smooth differential system can bifurcate more limit cycles than the smooth one.
These examples show that there exist more limit cycles in switching systems than continuous systems, and the dynamics of these systems is more complex.
Our result shows that planar piecewise smooth differential systems (3) and (4) can bifurcate three more limit cycles than the smooth one.
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If the coupling between two or more limit-cycle oscillators is relatively large, it can affect not only the phases but also the amplitudes, and a general theory of strongly interacting oscillators is likely to be no more or less complicated than a general theory of nonlinear systems.
With a further increase in the number of the learning steps, however, the number of fixed-point attractors begins to decrease, as these attractors are replaced by one or more limit-cycle attractors.
One more small-amplitude limit cycles near the origin can be found.
It is unlikely to have more small-amplitude limit cycles even using higher (varepsilon^{n} -order focus varepsilon^{n} -order
Despite a few interesting studies on more complicated dynamics such as limit cycles [56 58], invariant and limiting sets [59 64], LaSalle's invariance principle [65] and the Poincaré-Bendixson theorem [58, 60], much remains to be done for the qualitative theory, and especially the global dynamics, of impulsive semi-dynamical systems.
With the increase of attack angle, the deck section becomes much blunter, which leads to be more prone to limit cycle flutter (LCF).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com