On the dynamics of a nutrient–plankton system with Caputo and Caputo–Fabrizio fractional operators

Dehingia, Kaushik; Boulaaras, Salah; Gogoi, Suman

doi:10.1016/j.jocs.2024.102232

Journal of Computational Science

2024

DOI: 10.1016/j.jocs.2024.102232

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On the dynamics of a nutrient–plankton system with Caputo and Caputo–Fabrizio fractional operators

Kaushik Dehingia,

Salah Boulaaras,

Suman Gogoi

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Cited by 7 publications

References 37 publications

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Dynamic analysis of a class of fractional‐order dry friction oscillators

Si,

Xie,

Zhao

et al. 2024

Math Methods in App Sciences

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This article investigates a class of Duffing nonlinear dynamic systems with fractional‐order dry friction and conducts in‐depth research on the stability, chaotic characteristics, and erosion of the safety basin of this system; the results are verified through numerical simulation. First, the average method is used to approximate the amplitude–frequency relationship of the system, and the accuracy of the analytical results is verified through numerical experiments. Second, the Melnikov method is used to obtain the conditions for the system to enter chaos in the Smale horseshoe sense, and the Melnikov curve is drawn for further verification. Then, bifurcation diagrams are drawn for the changes in various parameters in the system, with a focus on analyzing the influence of friction factors on chaotic bifurcation. By applying the definition and calculation principle of the maximum Lyapunov exponent, and drawing and utilizing the maximum Lyapunov exponent graph, the chaotic state that the system enters under different parameters is more clearly defined. Finally, the evolution law of the safety basin under various parameter changes, especially dry friction changes, is analyzed, and the erosion and bifurcation mechanism of the safety basin is studied. Comparing with the bifurcation diagram, it reveals that chaos primarily contributes to the erosion of the safety basin.

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Dynamic analysis of a class of fractional‐order dry friction oscillators

Si,

Xie,

Zhao

et al. 2024

Math Methods in App Sciences

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Duality of multi-objective fractional Bi-level programming problem and its application

Saini,

Kailey

2024

OPSEARCH

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The Effect of Time Delay on the Dynamics of a Plankton-Nutrient System with Refuge

Dehingia,

Das,

Hinçal

et al. 2024

Braz J Phys

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On the dynamics of a nutrient–plankton system with Caputo and Caputo–Fabrizio fractional operators

Cited by 7 publications

References 37 publications

Dynamic analysis of a class of fractional‐order dry friction oscillators

Dynamic analysis of a class of fractional‐order dry friction oscillators

Duality of multi-objective fractional Bi-level programming problem and its application

The Effect of Time Delay on the Dynamics of a Plankton-Nutrient System with Refuge

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