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Patterns in a Time-Fractional Predator–Prey System with Finite Interaction Range^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Predator–Prey Model with Finite Interaction Length

#### Turing Instability Parameter Space

## 3. Fractional-Order System Stability Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Dispersion relation $\widehat{\lambda}\left(K\right)$ varying the parameter $\mu $. Several values of the ratio between the interaction lengths are presented with different color plots; values increase to the left of $\ell =$ 2 (blue), $\ell =$ 3 (green), $\ell =$ 5 (red), $\ell =$ 10 (dark purple), and $\ell =$ 20 (purple).

**Figure 2.**Stability curve ${\mu}_{c}$ as a function of ℓ with different fractional order values $\alpha $. To guarantee pattern formation $\mu $ must take values above the orange curve.

**Figure 3.**Intersection of the two surfaces ${\mu}_{c}$ and ${\mu}_{\alpha}$ in the extended parameter space for $0<\alpha <1$.

**Figure 4.**Alternative point of view of the intersection of the surfaces ${\mu}_{c}$ and ${\mu}_{\alpha}$.

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**MDPI and ACS Style**

Chacón-Acosta, G.; Núñez-López, M.
Patterns in a Time-Fractional Predator–Prey System with Finite Interaction Range. *Comput. Sci. Math. Forum* **2022**, *4*, 3.
https://doi.org/10.3390/cmsf2022004003

**AMA Style**

Chacón-Acosta G, Núñez-López M.
Patterns in a Time-Fractional Predator–Prey System with Finite Interaction Range. *Computer Sciences & Mathematics Forum*. 2022; 4(1):3.
https://doi.org/10.3390/cmsf2022004003

**Chicago/Turabian Style**

Chacón-Acosta, Guillermo, and Mayra Núñez-López.
2022. "Patterns in a Time-Fractional Predator–Prey System with Finite Interaction Range" *Computer Sciences & Mathematics Forum* 4, no. 1: 3.
https://doi.org/10.3390/cmsf2022004003