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A study on the dynamics of a nutrient-plankton-fish interaction model with Caputo fractional operator.

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Title: A study on the dynamics of a nutrient-plankton-fish interaction model with Caputo fractional operator.
Authors: Dehingia, Kaushik1,2,3 (AUTHOR), Farman, Muhammad2,4,5 (AUTHOR), Baluguri, Suresh Babu6 (AUTHOR), Hosseini, Kamyar2,7,8 (AUTHOR), Ghannam, Manal9 (AUTHOR), Choudhary, Santosh Kumar10 (AUTHOR) santosh.kumar@manipal.edu
Source: Fixed Point Theory & Algorithms for Sciences & Engineering. 4/17/2026, Vol. 2026 Issue 1, p1-33. 33p.
Subjects: Caputo fractional derivatives, Ecological models, Fractional calculus, Feedback control systems, Chaos theory, Stability of linear systems, Algal blooms, Interpolation
Abstract: The current study aims to fill a knowledge gap in the dynamics and regulation of algal blooms through fish predation, while accounting for the memory effect. A nutrient-phytoplankton-zooplankton-fish model using fractional derivatives in the Caputo sense is developed. The main conclusions are as follows. Reducing the fractional derivative order from 1.0 to 0.91 improves system stability by suppressing chaotic dynamics. Furthermore, the zooplankton death rate d 1 and fish population ingestion rate β were determined as bifurcation parameters. The linear feedback controller is effective at suppressing chaos. Simulations were performed using the Newton polynomial interpolation method. We investigated how the fractional derivative order affects system stability using arbitrarily chosen fractional parameter values. It was discovered that stability deteriorates near the co-axial equilibrium for lower zooplankton death rates. A higher maximal ingestion rate of fish destabilizes the system dynamics. Finally, phytoplankton's higher nutrient consumption rate reduces stability. Furthermore, higher-order fractional derivatives indicate lower stability, implying that systems with strong memory effects or history dependence are unstable. [ABSTRACT FROM AUTHOR]
Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: A study on the dynamics of a nutrient-plankton-fish interaction model with Caputo fractional operator.
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  Data: <searchLink fieldCode="AR" term="%22Dehingia%2C+Kaushik%22">Dehingia, Kaushik</searchLink><relatesTo>1,2,3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Farman%2C+Muhammad%22">Farman, Muhammad</searchLink><relatesTo>2,4,5</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Baluguri%2C+Suresh+Babu%22">Baluguri, Suresh Babu</searchLink><relatesTo>6</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Hosseini%2C+Kamyar%22">Hosseini, Kamyar</searchLink><relatesTo>2,7,8</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ghannam%2C+Manal%22">Ghannam, Manal</searchLink><relatesTo>9</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Choudhary%2C+Santosh+Kumar%22">Choudhary, Santosh Kumar</searchLink><relatesTo>10</relatesTo> (AUTHOR)<i> santosh.kumar@manipal.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22Fixed+Point+Theory+%26+Algorithms+for+Sciences+%26+Engineering%22">Fixed Point Theory & Algorithms for Sciences & Engineering</searchLink>. 4/17/2026, Vol. 2026 Issue 1, p1-33. 33p.
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  Data: <searchLink fieldCode="DE" term="%22Caputo+fractional+derivatives%22">Caputo fractional derivatives</searchLink><br /><searchLink fieldCode="DE" term="%22Ecological+models%22">Ecological models</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+calculus%22">Fractional calculus</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stability+of+linear+systems%22">Stability of linear systems</searchLink><br /><searchLink fieldCode="DE" term="%22Algal+blooms%22">Algal blooms</searchLink><br /><searchLink fieldCode="DE" term="%22Interpolation%22">Interpolation</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: The current study aims to fill a knowledge gap in the dynamics and regulation of algal blooms through fish predation, while accounting for the memory effect. A nutrient-phytoplankton-zooplankton-fish model using fractional derivatives in the Caputo sense is developed. The main conclusions are as follows. Reducing the fractional derivative order from 1.0 to 0.91 improves system stability by suppressing chaotic dynamics. Furthermore, the zooplankton death rate d 1 and fish population ingestion rate β were determined as bifurcation parameters. The linear feedback controller is effective at suppressing chaos. Simulations were performed using the Newton polynomial interpolation method. We investigated how the fractional derivative order affects system stability using arbitrarily chosen fractional parameter values. It was discovered that stability deteriorates near the co-axial equilibrium for lower zooplankton death rates. A higher maximal ingestion rate of fish destabilizes the system dynamics. Finally, phytoplankton's higher nutrient consumption rate reduces stability. Furthermore, higher-order fractional derivatives indicate lower stability, implying that systems with strong memory effects or history dependence are unstable. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Fixed Point Theory & Algorithms for Sciences & Engineering is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1186/s13663-026-00836-6
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Ecological models
        Type: general
      – SubjectFull: Fractional calculus
        Type: general
      – SubjectFull: Feedback control systems
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      – SubjectFull: Chaos theory
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      – SubjectFull: Stability of linear systems
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      – SubjectFull: Algal blooms
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      – SubjectFull: Interpolation
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              Text: 4/17/2026
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