Complex Dynamics in a Tritrophic Chain Model With Prey Stage Structure.
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| Title: | Complex Dynamics in a Tritrophic Chain Model With Prey Stage Structure. |
|---|---|
| Authors: | Blé, Gamaliel1 (AUTHOR), Dela-Rosa, Miguel Angel2 (AUTHOR) madelarosaca@secihti.mx, Loreto-Hernández, Iván2 (AUTHOR), Zhao, Hongyong (AUTHOR) zhaohy@nuaa.edu.cn |
| Source: | Journal of Applied Mathematics. 4/24/2026, Vol. 2026, p1-26. 26p. |
| Subjects: | Ecological models, Chaos theory, Predation, Frequencies of oscillating systems, Hopf bifurcations, Continuous time systems |
| Abstract: | A tritrophic chain model with prey stage structure (reproductive and nonreproductive classes) is analyzed. This model is provided by an ODE system of dimension four and the main premise consists in assuming that the interaction between reproductive population and predator is governed either by a functional response Holling type II or IV (where a defense mechanism is considered). The aim on the present paper is to show the dynamic richness of the model, which ranges from stable sets to chaotic behaviors. In fact, on each case, we show the parameter conditions for proving the validity of the analytic nondegeneracy hypotheses for having a nonresonant Hopf–Hopf bifurcation (HHB), and whose unfolding will have a normal form determined by the cubic normal coefficients associated to the corresponding truncated amplitude system. Derived from our analytic results, it is also shown by using numerical simulations that the coexistence of the species takes place by means of invariant sets with a more complex dynamics than the one given by a stable limit cycle. In fact, we show the existence of quasiperiodic orbits, of ω‐limit sets coming from an invariant two dimensional torus and of orbits with a chaotic motion. Finally, the contribution of our theoretical and numerical findings is appreciated in two directions: We provide a continuous dynamical system with chaotic behavior, and the coexistence of all the populations is obtained by means of interesting invariant sets that complement those obtained in previous published works by using stable equilibrium points and periodic orbits. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 193256026 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Complex Dynamics in a Tritrophic Chain Model With Prey Stage Structure. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Blé%2C+Gamaliel%22">Blé, Gamaliel</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Dela-Rosa%2C+Miguel+Angel%22">Dela-Rosa, Miguel Angel</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> madelarosaca@secihti.mx</i><br /><searchLink fieldCode="AR" term="%22Loreto-Hernández%2C+Iván%22">Loreto-Hernández, Iván</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhao%2C+Hongyong%22">Zhao, Hongyong</searchLink> (AUTHOR)<i> zhaohy@nuaa.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Applied+Mathematics%22">Journal of Applied Mathematics</searchLink>. 4/24/2026, Vol. 2026, p1-26. 26p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Ecological+models%22">Ecological models</searchLink><br /><searchLink fieldCode="DE" term="%22Chaos+theory%22">Chaos theory</searchLink><br /><searchLink fieldCode="DE" term="%22Predation%22">Predation</searchLink><br /><searchLink fieldCode="DE" term="%22Frequencies+of+oscillating+systems%22">Frequencies of oscillating systems</searchLink><br /><searchLink fieldCode="DE" term="%22Hopf+bifurcations%22">Hopf bifurcations</searchLink><br /><searchLink fieldCode="DE" term="%22Continuous+time+systems%22">Continuous time systems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: A tritrophic chain model with prey stage structure (reproductive and nonreproductive classes) is analyzed. This model is provided by an ODE system of dimension four and the main premise consists in assuming that the interaction between reproductive population and predator is governed either by a functional response Holling type II or IV (where a defense mechanism is considered). The aim on the present paper is to show the dynamic richness of the model, which ranges from stable sets to chaotic behaviors. In fact, on each case, we show the parameter conditions for proving the validity of the analytic nondegeneracy hypotheses for having a nonresonant Hopf–Hopf bifurcation (HHB), and whose unfolding will have a normal form determined by the cubic normal coefficients associated to the corresponding truncated amplitude system. Derived from our analytic results, it is also shown by using numerical simulations that the coexistence of the species takes place by means of invariant sets with a more complex dynamics than the one given by a stable limit cycle. In fact, we show the existence of quasiperiodic orbits, of ω‐limit sets coming from an invariant two dimensional torus and of orbits with a chaotic motion. Finally, the contribution of our theoretical and numerical findings is appreciated in two directions: We provide a continuous dynamical system with chaotic behavior, and the coexistence of all the populations is obtained by means of interesting invariant sets that complement those obtained in previous published works by using stable equilibrium points and periodic orbits. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Applied Mathematics is the property of Wiley-Blackwell 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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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1155/jama/6642738 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 26 StartPage: 1 Subjects: – SubjectFull: Ecological models Type: general – SubjectFull: Chaos theory Type: general – SubjectFull: Predation Type: general – SubjectFull: Frequencies of oscillating systems Type: general – SubjectFull: Hopf bifurcations Type: general – SubjectFull: Continuous time systems Type: general Titles: – TitleFull: Complex Dynamics in a Tritrophic Chain Model With Prey Stage Structure. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Blé, Gamaliel – PersonEntity: Name: NameFull: Dela-Rosa, Miguel Angel – PersonEntity: Name: NameFull: Loreto-Hernández, Iván – PersonEntity: Name: NameFull: Zhao, Hongyong IsPartOfRelationships: – BibEntity: Dates: – D: 24 M: 04 Text: 4/24/2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 1110757X Numbering: – Type: volume Value: 2026 Titles: – TitleFull: Journal of Applied Mathematics Type: main |
| ResultId | 1 |
