| Citation: |
Hefei Zhao, Kuilin Wu. LIMIT CYCLES FOR PIECEWISE LINEAR SYSTEMS WITH IMPROPER NODE[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2720-2738. doi: 10.11948/20220555
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LIMIT CYCLES FOR PIECEWISE LINEAR SYSTEMS WITH IMPROPER NODE
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Abstract
This paper is concerned with the number of limit cycles of planar piecewise linear systems for improper node-improper node and improper node-node types with a straight line of separation. We obtain some sufficient conditions for the existence and stability of limit cycles and prove that the systems have at least two nested limit cycles in some parameter regions.
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Keywords:
- Limit cycle /
- piecewise linear system /
- improper node
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References
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Hefei Zhao, Kuilin Wu. LIMIT CYCLES FOR PIECEWISE LINEAR SYSTEMS WITH IMPROPER NODE[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2720-2738. doi: 10.11948/20220555
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Figure 1.
Illustration of
$ P_L(y^-_0) $ $ P_R(y^+_0) $ $ b>0 $ -
Figure 2.
Illustration of
$ \textbf{D}_1(y_{0};b) $ -
Figure 3.
Graphs of
$ P_L $ $ P_R^{-1}|_{b>0} $ $ y_m^- \leq y_m^+ + b <0 $ $ T^+ >0> T^- $ $ b \in (0, \; b_m) $