Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect
This study examines a Caputo-type fractional-order food chain model, considering the Holling type II functional response with the vigilance effect. The model explores the interaction dynamics of the food chain model, which consists of prey, middle predators, and top predators. Additionally, habitat...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/9/1/45 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832588442580549632 |
|---|---|
| author | Vinoth Seralan Rajarathinam Vadivel Nallappan Gunasekaran Taha Radwan |
| author_facet | Vinoth Seralan Rajarathinam Vadivel Nallappan Gunasekaran Taha Radwan |
| author_sort | Vinoth Seralan |
| collection | DOAJ |
| description | This study examines a Caputo-type fractional-order food chain model, considering the Holling type II functional response with the vigilance effect. The model explores the interaction dynamics of the food chain model, which consists of prey, middle predators, and top predators. Additionally, habitat complexity is integrated into the model, which is assumed to reduce predation rates by lowering the encounter rates between predators and prey. All possible feasible equilibrium points are determined and the stability of our proposed model is explored near the equilibrium points. To support the analytical findings, numerical simulation results are given in terms of time series, phase portraits, and bifurcation diagrams. It is discovered that the proposed model can become more stable under a fractional-order derivative. Moreover, the interplay between the vigilance effect and habitat complexity is shown to influence the existence of stable and periodic dynamics. |
| format | Article |
| id | doaj-art-c43528b2ffd149529f893e30d60a5dac |
| institution | Kabale University |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj-art-c43528b2ffd149529f893e30d60a5dac2025-01-24T13:33:29ZengMDPI AGFractal and Fractional2504-31102025-01-01914510.3390/fractalfract9010045Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance EffectVinoth Seralan0Rajarathinam Vadivel1Nallappan Gunasekaran2Taha Radwan3Center for Nonlinear and Complex Networks, SRM Institute of Science and Technology, Ramapuram, Chennai 600089, Tamilnadu, IndiaDepartment of Mathematics, Faculty of Science and Technology, Phuket Rajabhat University, Phuket 83000, ThailandEastern Michigan Joint College of Engineering, Beibu Gulf University, Qinzhou 535011, ChinaDepartment of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi ArabiaThis study examines a Caputo-type fractional-order food chain model, considering the Holling type II functional response with the vigilance effect. The model explores the interaction dynamics of the food chain model, which consists of prey, middle predators, and top predators. Additionally, habitat complexity is integrated into the model, which is assumed to reduce predation rates by lowering the encounter rates between predators and prey. All possible feasible equilibrium points are determined and the stability of our proposed model is explored near the equilibrium points. To support the analytical findings, numerical simulation results are given in terms of time series, phase portraits, and bifurcation diagrams. It is discovered that the proposed model can become more stable under a fractional-order derivative. Moreover, the interplay between the vigilance effect and habitat complexity is shown to influence the existence of stable and periodic dynamics.https://www.mdpi.com/2504-3110/9/1/45food chainhabitat complexitystabilityfractional derivativesvigilance |
| spellingShingle | Vinoth Seralan Rajarathinam Vadivel Nallappan Gunasekaran Taha Radwan Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect Fractal and Fractional food chain habitat complexity stability fractional derivatives vigilance |
| title | Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect |
| title_full | Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect |
| title_fullStr | Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect |
| title_full_unstemmed | Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect |
| title_short | Dynamics of Fractional-Order Three-Species Food Chain Model with Vigilance Effect |
| title_sort | dynamics of fractional order three species food chain model with vigilance effect |
| topic | food chain habitat complexity stability fractional derivatives vigilance |
| url | https://www.mdpi.com/2504-3110/9/1/45 |
| work_keys_str_mv | AT vinothseralan dynamicsoffractionalorderthreespeciesfoodchainmodelwithvigilanceeffect AT rajarathinamvadivel dynamicsoffractionalorderthreespeciesfoodchainmodelwithvigilanceeffect AT nallappangunasekaran dynamicsoffractionalorderthreespeciesfoodchainmodelwithvigilanceeffect AT taharadwan dynamicsoffractionalorderthreespeciesfoodchainmodelwithvigilanceeffect |