TY - JOUR
T1 - Chaotic Dynamics of the Fractional Order Predator-Prey Model Incorporating Gompertz Growth on Prey with Ivlev Functional Response
AU - Santra, P. K.
AU - Uddin, Md. Jasim
AU - Rana, Sarker Md Sohel
AU - Mahapatra, G.s.
PY - 2024
DA - July
DO - 10.51537/chaos.1300754
JF - Chaos Theory and Applications
JO - CHTA
PB - Akif AKGÜL
WT - DergiPark
SN - 2687-4539
SP - 192
EP - 204
VL - 6
IS - 3
LA - en
AB - This paper examines dynamic behaviours of a two-species discrete fractional order predator-prey system with functional response form of Ivlev along with Gompertz growth of prey population. A discretization scheme is first applied to get Caputo fractional differential system for the prey-predator model. This study identifies certain conditions for the local asymptotic stability at the fixed points of the proposed prey-predator model. The existence and direction of the period-doubling bifurcation, Neimark-Sacker bifurcation, and Control Chaos are examined for the discrete-time domain. As the bifurcation parameter increases, the system displays chaotic behaviour. For various model parameters, bifurcation diagrams, phase portraits, and time graphs are obtained. Theoretical predictions and long-term chaotic behaviour are supported by numerical simulations across a wide variety of parameters. This article aims to offer an OGY and state feedback strategy that can stabilize chaotic orbits at a precarious equilibrium point.
KW - Prey-predator
model
KW - Fractional order
KW - Bifurcations
KW - Maximum Lyapunov
Exponents
KW - Fractal dimensions
KW - Chaos control
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UR - https://doi.org/10.51537/chaos.1300754
L1 - https://dergipark.org.tr/en/download/article-file/3158438
ER -