Results 41 to 50 of about 806 (167)

Bifurcation Analysis of Bogdanov-Takens Bifurcations in Delay Differential Equations [PDF]

In this paper, we will perform the parameter-dependent center manifold reduction near the generic and transcritical codimension two Bogdanov-Takens bifurcation in classical delay differential equations.
Kuznetsov, Yu. A., Bosschaert, M.M., Kuznetsov, Yu A., BOSSCHAERT, Maikel   +3 more
core   +2 more sources

Bogdanov-Takens and Triple Zero Bifurcations of a Delayed Modified Leslie-Gower Predator Prey System

Abstract and Applied Analysis, 2013
A delayed modified Leslie-Gower predator prey system with nonlinear harvesting is considered. The existence conditions that an equilibrium is Bogdanov-Takens (BT) or triple zero singularity of the system are given. By using the center manifold reduction,
Xia Liu, Jinling Wang
doaj   +1 more source

The Effects of Fluctuating Carrying Capacity on the Dynamics of a Holling‐Type III Predator–Prey Model

Journal of Mathematics, Volume 2026, Issue 1, 2026.
This study investigates the complex dynamics of a predator–prey system governed by the classical Lotka–Volterra model incorporating a Holling‐type III. To capture environmental variability, the prey’s carrying capacity is modeled as a periodic function, introducing a time‐dependent forcing into the system.
Ali Sarrah, Faizah J. Alanazi, Mehmet Yavuz, Sayed Saber, Mengxin Chen   +4 more
wiley   +1 more source

Degenerate Bogdanov-Takens bifurcations in a one-dimensional transport model of a fusion plasma [PDF]

, 2016
Experiments in tokamaks (nuclear fusion reactors) have shown two modes of operation: L-mode and H-mode. Transitions between these two modes have been observed in three types: sharp, smooth and oscillatory.
Mathematical Modeling, Kuznetsov, Yu.A., Pekkér, M.J., Sub Mathematical Modeling, Veldman, D.W.M., de Blank, H.J.   +5 more
core   +2 more sources

Nonlinear dynamics in a fear‐driven predator–prey system: Bistability, bifurcations, hydra effect, and optimal harvesting

Mathematical Methods in the Applied Sciences, Volume 48, Issue 2, Page 2194-2223, 30 January 2025.
The impact of predator‐driven fear on ecosystems is significant and can encompass both trophic (direct) and nontrophic (indirect) effects. Previous studies have shown that nontrophic fear effects have an important role in predator–prey dynamics. This study investigates the nontrophic fear effect on prey caused by generalist predators and explores ...
Anuj Kumar Umrao, Sonu Lamba, Prashant K. Srivastava   +2 more
wiley   +1 more source

Local Bifurcation and Global Stability of Two‐Prey‐One‐Predator Model

International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.
This paper deals with dynamical analysis of an ecological model. This model includes two logistically growing prey species, namely, Prey X and Prey Y, and the third species Z behaves as the predator, predating both Prey X and Prey Y according to the extended Holling type‐II functional response.
Hanaa Jamal Ahmed, Kawther Yusuf Abdulrahman, Karzan Abdulrahman Hamzah, Arkan Nawzad Mustafa, Mohamed A. Eltaher   +4 more
wiley   +1 more source

On uniqueness of limit cycles in general Bogdanov-Takens bifurcation

, 2021
In this paper we present a complete study to the well-known Bogdanov-Takens bifurcation and give a rigorous proof for the uniqueness of limit ...
Han, Maoan, Yang, Junmin, Llibre, Jaume
core  

Bifurcation in a Leslie–Gower system with fear in predators and strong Allee effect in prey

Nonlinear Analysis
In this paper, we consider a modified Leslie–Gower predator–prey model with Allee effect on prey and fear effect on predators. Results show complex dynamical behaviors in the model with these factors.
Ranchao Wu, Wenkai Xiong
doaj   +1 more source

Hydra Effect and Harvesting Optimal Policy in a Generalist Predator Prey Model With General Holling Type Response Functions

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
This study illustrates selective and combined harvesting efforts to examine the existence of hydra effect and global MSTY (maximum sustainable total yield) in a generalist predator–prey mathematical model with general Holling type response functions. The hydra effect is an ecological paradox in which a species’ population size increases in response to ...
Solomon Molla Alemu, Mohammed Yiha Dawed, Tesfaye Tefera Mamo, Theodore Simos   +3 more
wiley   +1 more source

Dynamical Analysis of a Delay Two‐Prey–One‐Predator Model Incorporating Fear Effect in the Growth Rate of Preys

Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.
In an ecological point of view, fears from predator cause physiological changes of prey population and these physiological changes may reduce the reproduction of prey. This paper deals with studying the effect of fear that is incorporated in the growth rate of prey on the dynamics of a delay ecological model consisting of two logistically growing prey ...
Hersh Aziz Mohammed, Arkan Nawzad Mustafa, Oluwole D. Makinde   +2 more
wiley   +1 more source