Material recycling in a closed aquatic ecosystem. II. Bifurcation analysis of a simple food-chain model

1996 ◽  
Vol 58 (5) ◽  
pp. 983-1000 ◽  
Author(s):  
Tibor Kmeť
Keyword(s):  
Bifurcation Analysis ◽  
Food Chain ◽  
Aquatic Ecosystem ◽  
Chain Model ◽  
Material Recycling ◽  
Food Chain Model

scholarly journals Bifurcation Analysis of a Discrete Food Chain Model with Harvesting

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Abdul Qadeer Khan ◽  
Shahid Mehmood Qureshi
Keyword(s):  
Fixed Points ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Periodic Points ◽  
Chain Model ◽  
Prime Period ◽  
Food Chain Model ◽  
Theoretical Results

We explore existence of fixed points, topological classifications around fixed points, existence of periodic points and prime period, and bifurcation analysis of a three-species discrete food chain model with harvesting. Finally, theoretical results are numerically verified.

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Fear

2018 ◽  
Vol 28 (01) ◽  
pp. 1850009 ◽  
Author(s):  
Pijush Panday ◽  
Nikhil Pal ◽  
Sudip Samanta ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Limit Cycles ◽  
Equilibrium Analysis ◽  
Chain Model ◽  
Maximum Lyapunov Exponent ◽  
The Cost ◽  
Food Chain Model

In the present paper, we investigate the impact of fear in a tri-trophic food chain model. We propose a three-species food chain model, where the growth rate of middle predator is reduced due to the cost of fear of top predator, and the growth rate of prey is suppressed due to the cost of fear of middle predator. Mathematical properties such as equilibrium analysis, stability analysis, bifurcation analysis and persistence have been investigated. We also describe the global stability analysis of the equilibrium points. Our numerical simulations reveal that cost of fear in basal prey may exhibit bistability by producing unstable limit cycles, however, fear in middle predator can replace unstable limit cycles by a stable limit cycle or a stable interior equilibrium. We observe that fear can stabilize the system from chaos to stable focus through the period-halving phenomenon. We conclude that chaotic dynamics can be controlled by the fear factors. We apply basic tools of nonlinear dynamics such as Poincaré section and maximum Lyapunov exponent to identify the chaotic behavior of the system.

Stability and Bifurcation Analysis of a Three-Species Food Chain Model with Delay

2015 ◽  
Vol 25 (09) ◽  
pp. 1550123 ◽  
Author(s):  
Nikhil Pal ◽  
Sudip Samanta ◽  
Santanu Biswas ◽  
Marwan Alquran ◽  
Kamel Al-Khaled ◽  
...  
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Bifurcation Analysis ◽  
Food Chain ◽  
Period Doubling ◽  
Equilibrium Analysis ◽  
Chain Model ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Food Chain Model

In the present paper, we study the effect of gestation delay on a tri-trophic food chain model with Holling type-II functional response. The essential mathematical features of the proposed model are analyzed with the help of equilibrium analysis, stability analysis, and bifurcation theory. Considering time-delay as the bifurcation parameter, the Hopf-bifurcation analysis is carried out around the coexisting equilibrium. The direction of Hopf-bifurcation and the stability of the bifurcating periodic solutions are determined by applying the normal form theory and center manifold theorem. We observe that if the magnitude of the delay is increased, the system loses stability and shows limit cycle oscillations through Hopf-bifurcation. The system also shows the chaotic dynamics via period-doubling bifurcation for further enhancement of time-delay. Our analytical findings are illustrated through numerical simulations.

Bifurcation Analysis for a Food Chain Model with Nonmonotonic Nutrition Conversion Rate of Predator to Top Predator

2020 ◽  
Vol 30 (08) ◽  
pp. 2050113
Author(s):  
Shaoli Wang ◽  
Xiao Wang ◽  
Xiaotian Wu
Keyword(s):  
Bifurcation Analysis ◽  
Food Chain ◽  
Conversion Rate ◽  
Chain Model ◽  
Top Predator ◽  
Saddle Node Bifurcation ◽  
Bifurcation Phenomena ◽  
Extinction Threshold ◽  
Nonmonotonic Functional Response ◽  
Food Chain Model

In this paper, a prey–predator-top predator food chain model with nonmonotonic functional response in the predators is studied. With an emphasis on the nutrition conversion rate of predator to top predator, one can get two important thresholds: the top predator extinction threshold and the coexistence threshold. The top predator will die out if the nutrition conversion rate of predator to top predator is less than the top predator extinction threshold; the prey, predator and top predator will coexist if the rate is larger than the coexistence threshold. While between the two thresholds is a bistable interval. When the nutrition conversion rate of predator to top predator is in the bistable interval, the system will see the emergence of bistability. The bifurcation analysis of the system depending on parameters indicates that it exhibits saddle-node bifurcation and Hopf bifurcation phenomena.

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