The Fractional Discrete Predator–Prey Model: Chaos, Control and Synchronization

Saadeh, Rania; Abbes, Abderrahmane; Al-Husban, Abdallah; Ouannas, Adel; Grassi, Giuseppe

doi:10.3390/fractalfract7020120

Cited by 32 publications

(20 citation statements)

References 26 publications

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“…However, various mathematical model options can be explored for future investigations. Potential directions for model development include a difference model [36][37][38], fractional difference [39,40], fractional differential [41,42], and partial differential [43][44][45]. Given that the data obtained in applications are discrete in time, the inclusion of a difference- Srinivas et al [24] developed a mathematical model for predator-prey dynamics in marine reserves and harvesting areas considering both immature and mature predator species.…”

Section: 𝐸 (𝑢) = 𝛼 (𝑡) − 𝛽 (𝑡)mentioning

confidence: 99%

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

et al. 2023

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The United Nations has predicted the growth of the human population to reach 8.405 billion by mid-2023, which is a 70% increase in global food demand. This growth will significantly affect global food security, mainly marine resources. Most marine resources exist within complex biological food webs, including predator–prey interactions. These interactions have been researched for decades by mathematicians, who have spent their efforts developing realistic and applicable models. Therefore, this paper systematically reviews articles related to predator–prey models considering the harvesting of resources in marine protected areas. The review identifies future remodeling problems using several mathematical tools. It also proposes the use of feedback linearization consisting of both the approximation and exact methods as an alternative to Jacobian linearization. The results show that in an optimal control analysis, adding a constraint in the form of population density greater than or equal to the positive threshold value should be considered to ensure an ecologically sustainable policy. This research and future developments in this area can significantly contribute to achieving the Sustainable Development Goals (SDGs) set for 2030.

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Section: 𝐸 (𝑢) = 𝛼 (𝑡) − 𝛽 (𝑡)mentioning

confidence: 99%

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

et al. 2023

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“…Shatnawi and Abbes et al [18] studied the multistability of fractional discrete memristor based map. Saadeh and Abbes et al [19] discussed a fractional discrete predatorprey model and its synchronization control. Sahoo and Roy et al [20] proposed a multi-wing chaotic attractor with unusual variation.…”

Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional multi-wing chaotic system

Wang

2023

Phys. Scr.

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The objective of this article is to obtain multi-wing chaotic attractors of fractional chaotic systems through computerized symbolic computation. By applying the Julia fractal technique, the different number wing attractors are constructed for proposed equations. Moreover, the dynamics of the multi-wing system are analyzed by phase diagram, Poincare mapping, etc Consequently, the system exhibits complex dynamics, and the motion states at different order can be known from the bifurcation diagram with the change of order. Additionally, aiming at multi- wing fractional chaotic system, the controllers are designed, and the finite time synchronization control of the proposed system is performed. The results prove that the proposed finite-time synchronization method has important research value in the field of engineering.

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“…As a consequence of these works, there has been an increase in the development of commensurate and incommensurate fractional discrete chaotic systems, as seen in [6][7][8][9][10][11][12][13] and references therein. Additionally, various control strategies and synchronization schemes have been proposed to synchronize different fractional chaotic maps [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Complexity and Chaos Analysis for Two-Dimensional Discrete-Time Predator–Prey Leslie–Gower Model with Fractional Orders

Hamadneh

Abbes

Falahah

et al. 2023

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The paper introduces a novel two-dimensional fractional discrete-time predator–prey Leslie–Gower model with an Allee effect on the predator population. The model’s nonlinear dynamics are explored using various numerical techniques, including phase portraits, bifurcations and maximum Lyapunov exponent, with consideration given to both commensurate and incommensurate fractional orders. These techniques reveal that the fractional-order predator–prey Leslie–Gower model exhibits intricate and diverse dynamical characteristics, including stable trajectories, periodic motion, and chaotic attractors, which are affected by the variance of the system parameters, the commensurate fractional order, and the incommensurate fractional order. Finally, we employ the 0–1 method, the approximate entropy test and the C0 algorithm to measure complexity and confirm chaos in the proposed system.

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The Fractional Discrete Predator–Prey Model: Chaos, Control and Synchronization

Cited by 32 publications

References 26 publications

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

Harvested Predator–Prey Models Considering Marine Reserve Areas: Systematic Literature Review

Finite-time synchronization of fractional multi-wing chaotic system

Complexity and Chaos Analysis for Two-Dimensional Discrete-Time Predator–Prey Leslie–Gower Model with Fractional Orders

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