# Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Background and Literature

## 2. Primary Outcomes

**Proposition**

**1.**

**Theorem**

**1.**

## 3. M($\mathbf{\xi}$) Represented Algebraically through Mathematical Analysis

**Lemma**

**1.**

**Proof.**

**Proposition**

**2.**

**Proof.**

**Lemma**

**2.**

**Proof.**

## 4. Establishing Theorem 1

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**A state sketch of Equation ${\left(\right)}_{\left(}$. For the sake of simplicity in its understanding we considered $\nu =x$ and $\beta =y$.

**Figure 2.**The shut trajectory of Equation ${\left(\right)}_{\left(}$. For the sake of simplicity in its understanding we considered $\nu =x$ and $\beta =y$.

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**MDPI and ACS Style**

Zhang, E.; Yang, J.; Shateyi, S.
Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions. *Mathematics* **2023**, *11*, 4555.
https://doi.org/10.3390/math11214555

**AMA Style**

Zhang E, Yang J, Shateyi S.
Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions. *Mathematics*. 2023; 11(21):4555.
https://doi.org/10.3390/math11214555

**Chicago/Turabian Style**

Zhang, Erli, Jihua Yang, and Stanford Shateyi.
2023. "Bifurcating Limit Cycles with a Perturbation of Systems Composed of Piecewise Smooth Differential Equations Consisting of Four Regions" *Mathematics* 11, no. 21: 4555.
https://doi.org/10.3390/math11214555