Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Din, Qamar; Rafaqat, Muhammad; Elsadany, A. A.; Zeng, Yanqiu

doi:10.1109/access.2020.3008522

Cited by 23 publications

(6 citation statements)

References 61 publications

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“…Then in 2017, Kon [1] examined the Leslie multispecies semelparous matrix model which has an arbitrary number of age classes. Then, there are also studies on multispecies but with other methods using the Rosenzweig-MacArthur model (See [14], [15]), the Leslie-Gower model (See [16], [17]), and the Lotka-Volterra model (See [18]- [20]).…”

Section: Introductionmentioning

confidence: 99%

Mathematical Model of Iteroparous and Semelparous Species Interaction

Hasibuan

Supriatna

Carnia

2022

CAUCHY

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A species can be categorized based on its reproductive strategy, including semelparous and iteroparous. Semelparous species is a species that reproduces only once in its lifetime shortly before dying, while iteroparous species is a species that reproduces in its lifetime more than once. In this paper, we examine multispecies growth dynamics involving both species categories focusing on one semelparous species and one iteroparous species influenced by density-dependent also harvesting in which there are two age classes each. We divided the study into two models comprising competitive and non-competitive models of both species. Competition in both species can consist of competition within the same species (intraspecific competition) and competition between different species (interspecific competition). Our results show that the level of competition both intraspecific and interspecific affects the co-existence equilibrium point and the local stability of the co-existence equilibrium point.

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Section: Introductionmentioning

confidence: 99%

Mathematical Model of Iteroparous and Semelparous Species Interaction

Hasibuan

Supriatna

Carnia

2022

CAUCHY

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“…Various functional responses have been derived and utilized, such as Holling type I to III [3][4][5], ratiodependent [6][7][8], Beddington-DeAngelis [9][10][11], and Crowley-Martin function response [12,13]. In modeling of population dynamics, two types of models are popular, namely discrete [14,15] and continuous-time models [11,13]. The interaction between two or more prey and predators is known to the food chain models.…”

Section: Introductionmentioning

confidence: 99%

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

Vinoth¹,

Sivasamy²,

Sathiyanathan³

et al. 2021

Adv Differ Equ

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Dynamical 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.

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“…Therefore, the several formulations for Lotka-Volterra systems and its variants can be utilized to describe many nonlinear interactions in other economic, physical and engineering systems. The study of possible dynamical behaviors and bifurcations of predator-prey system has attracted great research efforts of mathematical biologists and ecologists, see for example [7][8][9][10][11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

On discrete fractional-order Lotka-Volterra model based on the Caputo difference discrete operator

Elsonbaty

Elsadany

2021

Math Sci

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This work aims at introducing a new discrete fractional order model based on Lotka-Volterra prey-predator model with logistic growth of prey species. The proposed model is a generalization of the standard integer order discrete-time Lotka-Volterra model to its fractional-order version while incorporating also logistic growth for prey population. The equilibrium points of the presented model are firstly obtained, and their stability analysis is conducted. Then, the nonlinear dynamics of the proposed model and possible occurrence of chaotic behavior are explored. The effects of fractional order along with other key parameters in the model are investigated using several techniques. Thorough numerical simulations are carried out where Lyapunov exponents, bifurcation diagrams, phase portraits and as well as C 0 complexity measure are obtained to analyze the dynamics of the proposed model and confirm theoretical results.

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Dynamics and Chaos Control for a Discrete-Time Lotka-Volterra Model

Cited by 23 publications

References 61 publications

Mathematical Model of Iteroparous and Semelparous Species Interaction

Mathematical Model of Iteroparous and Semelparous Species Interaction

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

On discrete fractional-order Lotka-Volterra model based on the Caputo difference discrete operator

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