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Phase Curve and Vector Field for Piecewise Linear Liénard Systems

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This Demonstration shows plots of the phase curve and the vector field for a Liénard system of the form and , with and . In [1] Shimin Li and Jaume Llibre proved that there are 32 possible topological classes of phase portraits for this system.

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Drag the locator to select a phase curve through that point. Adjust the parameters , , in the differential equations and to observe the topological shifts in the phase portrait. The system has a unique equilibrium point . Accordingly, global stability is guaranteed if the eigenstates of the system's linear pieces are both stable.

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Contributed by: Celestine Preetham Lawrence (August 2022)
Open content licensed under CC BY-NC-SA

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[1] Shimin Li and Jaume Llibre, "Phase Portraits of Piecewise Linear Continuous Differential Systems with Two Zones Separated by a Straight Line," Journal of Differential Equations, 266(12), 2019 pp. 8094–8109. doi:10.1016/j.jde.2018.12.024.

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