Results 41 to 50 of about 2,171 (143)

Some Applications of Bifurcation Formulae to the Period Maps of Delay Differential Equations [PDF]

, 2005
Our purpose is to present some applications of the bifurcation formulae derived in [13] for periodic delay differential equations. We prove that a sequence of Neimark-Sacker bifurcations occurs as the parameter increases.
Röst, Gergely
core  

Complex Dynamics and Chaos Control of Discrete Prey–Predator Model With Caputo Fractional Derivative

Complexity, Volume 2025, Issue 1, 2025.
This work examines a discrete prey–predator model using the fractional derivative. The conditions for the existence and stability of the fixed points in the model are identified. The analysis is centered on exploring various bifurcations at the positive fixed point to understand their ecological implications.
Rowshon Ara, Sohel Rana S. M., Jesus Manuel Munoz-Pacheco   +2 more
wiley   +1 more source

Probability of local bifurcation type from a fixed point: A random matrix perspective

, 2005
Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal ...
A. Edelman, A. Edelman, A. Edelman, A. Edelman, A. Katok, B. Cessac, B. Doyon, B. Doyon, B. R. Hunt, B. R. Hunt, D. J. Albers, D. J. Albers, D. J. Albers, D. Ruelle, E. Kanzieper, F. Takens, J. C. Sprott, J. Ginbre, J. Neimark, K. Hornik, K. Hornik, M. Kac, O. Moynot, P. Brunovsky, R. Gencay, S. Amari, T. Sauer, V. Girko, V. Girko, V. Girko, V. Girko, V. Girko, V. Girko, V. Girko, V. I. Oseledec, W. Ott, W. Ott, Y. B. Pesin, Z. D. Bai   +38 more
core   +1 more source

A Study of Stability and Bifurcation in a Discretized Predator–Prey Model With Holling Type III Response and Prey Refuge Via Piecewise Constant Argument Method

Complexity, Volume 2025, Issue 1, 2025.
This study explores the dynamics of a discrete‐time predator–prey system, incorporating a Holling type III functional response and prey refuge, through the piecewise constant argument method. This method keeps things consistent and prevents negative population values, which is often a drawback of older techniques. We take a closer look at fixed points,
Faisal Alsharif, Rizwan Ahmed, Ibrahim Alraddadi, Mohammed Alsubhi, Muhammad Amer, Md. Jasim Uddin, Giacomo Innocenti   +6 more
wiley   +1 more source

Spatiotemporal Patterns Formed by a Discrete Nutrient-Phytoplankton Model with Time Delay

Complexity, 2020
In this research, a continuous nutrient-phytoplankton model with time delay and Michaelis–Menten functional response is discretized to a spatiotemporal discrete model.
Feifan Zhang, Wenjiao Zhou, Lei Yao, Xuanwen Wu, Huayong Zhang   +4 more
doaj   +1 more source

Bifurcation Dynamics and Complex Behavior in a Discrete‐Time Predator–Prey Model With Cross‐Species Interaction Incorporating Holling Type‐II Response

Complexity, Volume 2025, Issue 1, 2025.
We investigate the nonlinear dynamics of a discrete‐time predator–prey model governed by a Holling Type‐II functional response. Starting from a biologically motivated continuous‐time system, we derive its discrete analogue via the explicit Euler method and employ nondimensionalization to reduce the number of parameters.
Muhammad Rafaqat, Syed Tauseef Saeed, Salman Saleem, Feyisa Edosa Merga, Xinzhi Liu   +4 more
wiley   +1 more source

PD control at Neimark–Sacker bifurcations in a Mackey–Glass system

Advances in Difference Equations, 2018
This article focuses on a proportional-derivative (PD) feedback controller to control a Neimark–Sacker bifurcation for a Mackey–Glass system by the Euler method.
Yuanyuan Wang
doaj   +1 more source

Stability Analysis of a Discrete‐Time Predator–Prey Model Using Piecewise Constant Argument

Discrete Dynamics in Nature and Society, Volume 2025, Issue 1, 2025.
This paper offers a thorough analysis of the discrete‐time predator–prey model obtained by using the piecewise constant argument technique. Our principal findings demonstrate that the coexistence fixed exhibits rich dynamical behavior, undergoing both Neimark–Sacker and period‐doubling bifurcations as ecological parameters vary. These bifurcations lead
Muhammad Rafaqat, Abdou Al Zubaidi, Faisal Z. Duraihem, Jihad Younis, Syed Tauseef Saeed, Rodica Luca   +5 more
wiley   +1 more source

Fractional Order Plant‐Herbivore Dynamics: From Stability to Chaos Control

Discrete Dynamics in Nature and Society, Volume 2025, Issue 1, 2025.
This study investigates the dynamic behavior of a discrete‐time plant‐herbivore model incorporating conformable fractional‐order derivatives and a toxin‐dependent functional response. The model is discretized using a piecewise constant argument approach, enabling the analysis of memory effects and nonlocal interactions in ecological dynamics.
Güven Kaya, Hasan Gündüz, Mesut Karabacak, Ercan Çelik, Rigoberto Medina   +4 more
wiley   +1 more source

Neimark-Sacker-Turing Instability and Pattern Formation in a Spatiotemporal Discrete Predator-Prey System with Allee Effect

Discrete Dynamics in Nature and Society, 2018
A spatiotemporal discrete predator-prey system with Allee effect is investigated to learn its Neimark-Sacker-Turing instability and pattern formation.
Huayong Zhang, Xuebing Cong, Tousheng Huang, Shengnan Ma, Ge Pan   +4 more
doaj   +1 more source