TY  - JOUR
T1  - Numerical Solutions of Fractional Order Ratio-Dependent Food Chain Model with Caputo Derivative
TT  - Kesir Mertebeden Orana Bağlı Besin Zinciri Modelinin Caputo Türevi ile Sayısal Çözümleri
AU  - Öztürk, Zafer
PY  - 2025
DA  - October
Y2  - 2025
DO  - 10.29130/dubited.1600292
JF  - Duzce University Journal of Science and Technology
JO  - DÜBİTED
PB  - Düzce Üniversitesi
WT  - DergiPark
SN  - 2148-2446
SP  - 1544
EP  - 1555
VL  - 13
IS  - 4
LA  - en
AB  - The study of life within an ecosystem reveals a complex system. Ecosystems are characterised by the presence of all the elements that give rise to chaotic dynamics. Although chaos is often predicted by mathematical models, there is currently only limited evidence of its existence in nature, with the proof of its occurrence remaining scarce and uncertain. Despite the apparent simplicity of food chains, they exhibit highly complex dynamics. Models created several years ago have confirmed that food chains have complex dynamics. In this study, a fractional order ratio-dependent food chain model is considered. This model consists of three compartments: prey population density (𝑋), predator population density (𝑌) and top predator density (𝑍). The fractional derivative is employed in accordance with the Caputo sense. A mathematical analysis of the fractional order ratio-dependent food chain model is conducted. Numerical results are obtained with the aid of the Euler method and the graphs are interpreted.
KW  - Fractional Order Food Chain Model
KW  - Mathematical Modeling
KW  - Euler Method
KW  - Caputo Derivative
N2  - The study of life within an ecosystem reveals a complex system. Ecosystems are characterised by the presence of all the elements that give rise to chaotic dynamics. Although chaos is often predicted by mathematical models, there is currently only limited evidence of its existence in nature, with the proof of its occurrence remaining scarce and uncertain.  Despite the apparent simplicity of food chains, they exhibit highly complex dynamics. Models created several years ago have confirmed that food chains have complex dynamics. In this study, a fractional order rate-dependent food chain model is considered. This model consists of three compartments: prey population density (X), predator population density (Y) and top predator density (Z). The fractional derivative is employed in accordance with the Caputo sense. A mathematical analysis of the fractional order rate-dependent food chain model is conducted. Numerical results are obtained with the aid of the Euler method and the graphs are interpreted.
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UR  - https://doi.org/10.29130/dubited.1600292
L1  - https://dergipark.org.tr/tr/download/article-file/4435120
ER  -