The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation of the system results in periodic, quasi-periodic, chaotic and unbounded behavior. A Poincare map is constructed to simplify the mathematical analysis. The stability of the xed points of the Poincare map corresponding to period-one solutions is investigated. By varying the forcing parameters, we observed a saddle-center and a pitchfork bifurcation of two centers and a saddle type xed point. The global dynamics of the system is investigated, showing discontinuity induced bifurcations of the xed points.

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This preprint is available for download as a PDF.

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Posted 03 Mar, 2021

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###### Review #? received

Received 01 Mar, 2021

###### Reviewers invited

Invitations sent on 28 Feb, 2021

###### Editor assigned

On 15 Feb, 2021

###### First submitted

On 12 Feb, 2021

Posted 03 Mar, 2021

###### No community comments so far

###### Review #? received

Received 01 Mar, 2021

###### Reviewers invited

Invitations sent on 28 Feb, 2021

###### Editor assigned

On 15 Feb, 2021

###### First submitted

On 12 Feb, 2021

The dynamics of a hysteretic relay oscillator with harmonic forcing is investigated. Periodic excitation of the system results in periodic, quasi-periodic, chaotic and unbounded behavior. A Poincare map is constructed to simplify the mathematical analysis. The stability of the xed points of the Poincare map corresponding to period-one solutions is investigated. By varying the forcing parameters, we observed a saddle-center and a pitchfork bifurcation of two centers and a saddle type xed point. The global dynamics of the system is investigated, showing discontinuity induced bifurcations of the xed points.

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Figure 32

This preprint is available for download as a PDF.

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