Chaotic dynamics of a tri-topic food chain model with Beddington–DeAngelis functional response in presence of fear effect

Abstract The most important fact in the field of theoretical ecology and evolutionary biology is the strategy of predation for predators and the avoidance of prey from predator attack. A lot of experimental works suggest that the reduction of prey depends on both direct predation and fear of predation. We explore the impact of fear effect and mutual interference into a three-species food chain model. In this manuscript, we have considered a tri-topic food web model with Beddington-DeAngelis functional response between interacting species, incorporating the reduction of prey and intermediate predator growth because of the fear of intermediate and top predator respectively. We have provided parametric conditions on the existence of biologically feasible equilibria as well as their local and global stability also. We have established conditions of transcritical, saddle-node and Hopf bifurcation in vicinity of different equilibria. Finally, we performed some numerical investigations to justify analytical findings.Mathematics Subject Classification : 39A30, 92D25, 92D50.

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Bifurcation study and pattern formation analysis of a tritrophic food chain model with group defense and Ivlev-like nonmonotonic functional response

Chaos Solitons & Fractals ◽

10.1016/j.chaos.2021.110964 ◽

2021 ◽

Vol 147 ◽

pp. 110964

Author(s):

Vikas Kumar ◽

Nitu Kumari

Keyword(s):

Pattern Formation ◽

Functional Response ◽

Food Chain ◽

Chain Model ◽

Group Defense ◽

Nonmonotonic Functional Response ◽

Food Chain Model

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RICH DYNAMICS OF A TIME-DELAYED FOOD CHAIN MODEL

Journal of Biological System ◽

10.1142/s0218339006001921 ◽

2006 ◽

Vol 14 (03) ◽

pp. 387-412 ◽

Cited By ~ 2

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.

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Chaos in Ecology: The Topological Entropy of a Tritrophic Food Chain Model

Discrete Dynamics in Nature and Society ◽

10.1155/2008/541683 ◽

2008 ◽

Vol 2008 ◽

pp. 1-12 ◽

Cited By ~ 1

Author(s):

Jorge Duarte ◽

Cristina Januário ◽

Nuno Martins

Keyword(s):

Topological Entropy ◽

Food Chain ◽

Chaotic Dynamics ◽

Life Sciences ◽

Chain Model ◽

Parameter Region ◽

Complex Interactions ◽

Return Maps ◽

Food Chain Model ◽

Specific Food

An ecosystem is a web of complex interactions among species. With the purpose of understanding this complexity, it is necessary to study basic food chain dynamics with preys, predators and superpredators interactions. Although there is an elegant interpretation of ecological models in terms of chaos theory, the complex behavior of chaotic food chain systems is not completely understood. In the present work we study a specific food chain model from the literature. Using results from symbolic dynamics, we characterize the topological entropy of a family of logistic-like Poincaré return maps that replicates salient aspects of the dynamics of the model. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. This work is still another illustration of the role that the theory of dynamical systems can play in the study of chaotic dynamics in life sciences.

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