Complex dynamics of sexually reproductive generalist predator and gestation delay in a food chain model: double Hopf-bifurcation to Chaos

2016 ◽  
Vol 55 (1-2) ◽  
pp. 513-547 ◽  
Author(s):  
Rashmi Agrawal ◽  
Debaldev Jana ◽  
Ranjit Kumar Upadhyay ◽  
V. Sree Hari Rao
Keyword(s):  
Hopf Bifurcation ◽  
Food Chain ◽  
Complex Dynamics ◽  
Generalist Predator ◽  
Chain Model ◽  
Double Hopf Bifurcation ◽  
Gestation Delay ◽  
Food Chain Model

RICH DYNAMICS OF A TIME-DELAYED FOOD CHAIN MODEL

2006 ◽  
Vol 14 (03) ◽  
pp. 387-412 ◽  
Author(s):  
ALAKES MAITI ◽  
G. P. SAMANTA
Keyword(s):  
Computer Simulation ◽  
Time Delay ◽  
Functional Response ◽  
Food Chain ◽  
Complex Dynamics ◽  
Chain Model ◽  
Dynamical Behaviors ◽  
Discrete Time Delay ◽  
Food Chain Model ◽  
Practical Implications

Complex dynamics of a tritrophic food chain model is discussed in this paper. The model is composed of a logistic prey, a classical Lotka-Volterra functional response for prey-predator and a ratio-dependent functional response for predator-superpredator. Dynamical behaviors such as boundedness, stability and bifurcation of the model are studied critically. The effect of discrete time-delay on the model is investigated. Computer simulation of various solutions is presented to illustrate our mathematical findings. How these ideas illuminate some of the observed properties of real populations in the field is discussed and practical implications are explored.

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.

scholarly journals Complex dynamics of a three species food-chain model with Holling type IV functional response

2011 ◽  
Vol 16 (3) ◽  
pp. 553-374
Author(s):  
Ranjit Kumar Upadhyay ◽  
Sharada Nandan Raw
Keyword(s):  
Food Chain ◽  
Complex Dynamics ◽  
Chaotic Behavior ◽  
Period Doubling ◽  
Chain Model ◽  
Narrow Region ◽  
Type Iv ◽  
Numerical Bifurcation ◽  
Parameter Values ◽  
Food Chain Model

In this paper, dynamical complexities of a three species food chain model with Holling type IV predator response is investigated analytically as well as numerically. The local and global stability analysis is carried out. The persistence criterion of the food chain model is obtained. Numerical bifurcation analysis reveals the chaotic behavior in a narrow region of the bifurcation parameter space for biologically realistic parameter values of the model system. Transition to chaotic behavior is established via period-doubling bifurcation and some sequences of distinctive period-halving bifurcation leading to limit cycles are observed.

Stability and Bifurcation Analysis in a Food Chain Model with Delay

2011 ◽  
Vol 110-116 ◽  
pp. 3382-3388
Author(s):  
Zhang Li
Keyword(s):  
Hopf Bifurcation ◽  
Food Chain ◽  
Center Manifold ◽  
Chain Model ◽  
Center Manifold Theory ◽  
Stability And Bifurcation Analysis ◽  
Existence And Stability ◽  
The Stability ◽  
Manifold Theory ◽  
Food Chain Model

In this paper, we investigate a delayed three-species food chain model. The existence and stability of equilibria are obtained. A explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form and the center manifold theory.

Complex Dynamics Due to Multiple Limit Cycle Bifurcations in a Tritrophic Food Chain Model

2019 ◽  
Vol 29 (14) ◽  
pp. 1950193
Author(s):  
Xiangyu Wang ◽  
Pei Yu
Keyword(s):  
Food Chain ◽  
Limit Cycles ◽  
Complex Dynamics ◽  
Chain Model ◽  
Stable Limit ◽  
Normal Form Theory ◽  
Bistable Phenomenon ◽  
Multiple Limit Cycle ◽  
The Stability ◽  
Food Chain Model

In this paper, we consider a tritrophic food chain model with Holling functional response types III and IV for the predator and superpredator, respectively. The main attention is focused on the stability and bifurcation of equilibria when the prey has a linear growth. Coexistence of different species is shown in the food chain, demonstrating bistable phenomenon. Hopf bifurcation is studied to show complex dynamics due to multiple limit cycles bifurcation. In particular, normal form theory is applied to prove that three limit cycles can bifurcate from an equilibrium in the vicinity of a Hopf critical point, yielding a new bistable phenomenon which involves two stable limit cycles.

scholarly journals Complex dynamics in a tritrophic food chain model with general functional response

2020 ◽  
Vol 33 (2) ◽  
Author(s):  
Mohammed Y. Dawed ◽  
Patrick M. Tchepmo Djomegni ◽  
Harald E. Krogstad
Keyword(s):  
Functional Response ◽  
Food Chain ◽  
Complex Dynamics ◽  
Chain Model ◽  
Food Chain Model

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.

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