scholarly journals Pattern Formation in Spatially Extended Tritrophic Food Chain Model Systems: Generalist versus Specialist Top Predator

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Nitu Kumari
Keyword(s):  
Pattern Formation ◽  
Food Chain ◽  
Model System ◽  
Model Systems ◽  
Subsurface Water ◽  
Chain Model ◽  
Top Predator ◽  
Top Predators ◽  
Spatially Extended ◽  
Food Chain Model

The complex dynamics of two types of tritrophic food chain model systems when the species undergo spatial movements, modeling two real situations of marine ecosystem, are investigated in this study analytically and using numerical simulations. The study has been carried out with the objective to explore and compare the competitive effects of fish and molluscs species being the top predators, when phytoplankton and zooplankton species are undergoing spatial movements in the subsurface water. Reaction diffusion systems have been used to represent temporal evolution and spatial interaction among the species. The two model systems differ in an essential way that the top predators are generalist and specialist, respectively, in two models. “Wave of Chaos” mechanism is found to be the responsible factor for the pattern (non-Turing) formation in one dimension seen in the food chain ending with top generalist predator. In the present work we have reported WOC phenomenon, for the first time in the literature, in a three-species spatially extended food chain model system. The numerical simulation leads to spontaneous and interesting pattern formation in two dimensions. Constraints on different parameters under which Turing and non-Turing patterns may be observed are obtained analytically. Diffusion-driven analysis is carried out, and the effect of diffusion on the chaotic dynamics of the model systems is studied. The existence of chaotic attractor and long-term chaotic behavior demonstrate the effect of diffusion on the dynamics of the model systems. It is observed from numerical study that food chain model system with top predator as generalist has very rich dynamics and shows very interesting patterns. An ecosystem having top predator as specialist leads to the stability of the system.

DYNAMIC RELATIONSHIP BETWEEN THE MUTUAL INTERFERENCE AND GESTATION DELAYS OF A HYBRID TRITROPHIC FOOD CHAIN MODEL

2018 ◽  
Vol 59 (3) ◽  
pp. 370-401 ◽  
Author(s):  
RASHMI AGRAWAL ◽  
DEBALDEV JANA ◽  
RANJIT KUMAR UPADHYAY ◽  
V. SREE HARI RAO
Keyword(s):  
Functional Response ◽  
Food Chain ◽  
Model System ◽  
Mutual Interference ◽  
Model Systems ◽  
Chain Model ◽  
Top Predator ◽  
Functional Responses ◽  
Gestation Delay ◽  
Food Chain Model

We have proposed a three-species hybrid food chain model with multiple time delays. The interaction between the prey and the middle predator follows Holling type (HT) II functional response, while the interaction between the top predator and its only food, the middle predator, is taken as a general functional response with the mutual interference schemes, such as Crowley–Martin (CM), Beddington–DeAngelis (BD) and Hassell–Varley (HV) functional responses. We analyse the model system which employs HT II and CM functional responses, and discuss the local and global stability analyses of the coexisting equilibrium solution. The effect of gestation delay on both the middle and top predator has been studied. The dynamics of model systems are affected by both factors: gestation delay and the form of functional responses considered. The theoretical results are supported by appropriate numerical simulations, and bifurcation diagrams are obtained for biologically feasible parameter values. It is interesting from the application point of view to show how an individual delay changes the dynamics of the model system depending on the form of functional response.

scholarly journals Dynamical analysis of a delayed food chain model with additive Allee effect

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
S. Vinoth ◽  
R. Sivasamy ◽  
K. Sathiyanathan ◽  
Grienggrai Rajchakit ◽  
P. Hammachukiattikul ◽  
...  
Keyword(s):  
Food Chain ◽  
Allee Effect ◽  
Time Lag ◽  
Dynamical Analysis ◽  
Chain Model ◽  
Top Predator ◽  
Interior Equilibrium ◽  
Top Predators ◽  
Proposed Model ◽  
Food Chain Model

AbstractDynamical analysis of a delayed tri-trophic food chain consisting of prey, an intermediate, and a top predator is investigated in this paper. The additive Allee effect is introduced in the prey population, and it is assumed that there is a time lag due to the gestation effect in the intermediate predator. The interference among the prey and the intermediate predator is according to Holling type II, while the interaction between the intermediate and top predators follows the Crowley–Martin functional response. The local stability and bifurcation analysis of the proposed model at the interior equilibrium point are studied. Numerical simulations are provided to ensure the mathematical results.

scholarly journals ON NONLINEAR FRACTIONAL-ORDER MATHEMATICAL MODEL OF FOOD-CHAIN

Fractals ◽  
2021 ◽  
Author(s):  
KOTTAKKARAN SOOPPY NISAR ◽  
MATI UR RAHMAN ◽  
GHAYLEN LAOUINI ◽  
MESHAL SHUTAYWI ◽  
MUHAMMAD ARFAN
Keyword(s):  
Mathematical Model ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Fractional Order ◽  
Food Chain ◽  
Existence Results ◽  
Chain Model ◽  
Top Predator ◽  
The Fixed Point Theorem ◽  
Food Chain Model

This paper investigates the dynamical semi-analysis of the delayed food chain model under the considered fractional order. The food chain model is composed of three compartments, namely, population of the prey, intermediate predator and a top predator. By using the fixed point theorem approach, we exploit some conditions for existence results and stability for the considered system via Atangana–Baleanu–Caputo derivative with fractional order. Also, using the well-known Adam–Bashforth technique for numerics, we simulate the concerning results for the interference between the prey and intermediate predator. Graphical results are discussed for different fractional-order values for the considered model.

scholarly journals Dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries

2020 ◽  
Vol 15 ◽  
pp. 62
Author(s):  
Dawei Zhang ◽  
Beiping Duan ◽  
Binxiang Dai
Keyword(s):  
Food Chain ◽  
Dimensional Space ◽  
Chain Model ◽  
Time Behavior ◽  
Free Boundaries ◽  
Top Predator ◽  
Predator Species ◽  
Spreading And Vanishing ◽  
Ratio Dependent ◽  
Food Chain Model

This paper focuses on the dynamics of a three species ratio-dependent food chain model with diffusion and double free boundaries in one dimensional space, in which the free boundaries represent expanding fronts of top predator species. The existence, uniqueness and estimates of the global solution are discussed firstly. Then we prove a spreading–vanishing dichotomy, specifically, the top predator species either successfully spreads to the entire space as time t goes to infinity and survives in the new environment, or fails to establish and dies out in the long run. The long time behavior of the three species and criteria for spreading and vanishing are also obtained. Besides, our simulations illustrate the impacts of initial occupying area and expanding capability on the dynamics of top predator for free boundaries.

Dynamics of an autonomous food chain model and existence of global attractor of the associated non-autonomous system

2019 ◽  
Vol 12 (08) ◽  
pp. 1950082 ◽  
Author(s):  
Jyotirmoy Roy ◽  
Shariful Alam
Keyword(s):  
Hopf Bifurcation ◽  
Food Chain ◽  
Migration Rate ◽  
Equilibrium Points ◽  
Model System ◽  
Seasonal Effect ◽  
Chain Model ◽  
Upward Migration ◽  
Downward Migration ◽  
Food Chain Model

In this paper, we have analyzed a tri-trophic food chain model consisting of phytoplankton, zooplankton and fish population in an aquatic environment. Here, the pelagic water column is divided into two layers namely, the upper layer and the lower layer. The zooplankton population makes a diel vertical migration (DVM) from lower portion to upper portion and vice-versa to trade-off between food source and fear from predator (Fish). Here, mathematical model has been developed and analyzed in a rigorous way. Apart from routine calculations like boundedness and positivity of the solution, local stability of the equilibrium points, we performed Hopf bifurcation analysis of the interior equilibrium point of our model system in a systematic way. It is observed that the migratory behavior of zooplankton plays a crucial role in the dynamics of the model system. Both the upward and downward migration rates of DVM leads the system into Hopf bifurcation. The upward migration rate of zooplankton deteriorates the stable coexistence of all the species in the system, whereas the downward migration rate enhance the stability of the system. Further, we analyze the non-autonomous version of the system to capture seasonal effect of environmental variations. We have shown that under certain parametric restrictions periodic coexistence of all the species of our system is possible. Finally, extensive numerical simulation has been performed to support our analytical findings.

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