Flip and Neimark-Sacker Bifurcations of a Discrete Time Predator-Pre Model

Li, Yong; Rafaqat, Muhammad; Zia, Tariq Javed; Ahmed, Imran; Jung, Chahn Yong

doi:10.1109/access.2019.2937956

Cited by 7 publications

(4 citation statements)

References 35 publications

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“…Some classical results on bifurcations can be found in previous studies 1–5 . Many researchers over the last years provide a plethora of interesting results in this field; see, for example, other studies 6–13 …”

Section: Introductionmentioning

confidence: 82%

Neimark–Sacker, flip, and transcritical bifurcation in a close‐to‐symmetric system of difference equations with exponential terms

Mylona

Papaschinopoulos

Schinas

2021

Math Methods in App Sciences

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In this paper, we study the conditions under which the following close‐to‐symmetric system of difference equations with exponential terms: xn+1=a1ynb1+yn+c1xnek1−d1xn1+ek1−d1xn, yn+1=a2xnb2+xn+c2ynek2−d2yn1+ek2−d2yn where ai, bi, ci, di, and ki, for i=1,2, are real constants and the initial values x0 and y0 are real numbers, undergoes Neimark–Sacker, flip, and transcritical bifurcation. The analysis is conducted applying center manifold theory and the normal form bifurcation analysis.

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Section: Introductionmentioning

confidence: 82%

Neimark–Sacker, flip, and transcritical bifurcation in a close‐to‐symmetric system of difference equations with exponential terms

Mylona

Papaschinopoulos

Schinas

2021

Math Methods in App Sciences

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“…As shown in previous paragraph, the unstable region caused by a NS bifurcation was detected. The bifurcation happens when two complex conjugate Floquet multipliers reach unit modulus [28]. This region can be dangerous for the VM because the unexpected dynamics may occurs.…”

Section: Unstable Region Controlmentioning

confidence: 99%

Numerical study of a pendulum absorber/harvester system with a semi‐active suspension

Kęcik

2020

Z Angew Math Mech

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The paper presents numerical analysis of an absorber/harvester system installed on the semi‐active suspension. The pendulum tuned mass absorber has been modified by use of a magnetic levitation harvester. The primary goal is to mitigate the vibration of the primary structure and the secondary goal is to harvest energy out of the vibration absorber simultaneously. This system is strongly nonlinear and the unstable regions are detected. Therefore, to control the dynamic response the semi‐active suspension consisting of the magnetorheological (MR) damper and the shape memory alloy (SMA) spring is proposed. It is shown that with a proper configurations of parameters an effective energy harvesting can be obtained combined with vibration mitigation in the host system.

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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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Flip and Neimark-Sacker Bifurcations of a Discrete Time Predator-Pre Model

Cited by 7 publications

References 35 publications

Neimark–Sacker, flip, and transcritical bifurcation in a close‐to‐symmetric system of difference equations with exponential terms

Neimark–Sacker, flip, and transcritical bifurcation in a close‐to‐symmetric system of difference equations with exponential terms

Numerical study of a pendulum absorber/harvester system with a semi‐active suspension

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

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