Article
Engineering, Mechanical
Jianfeng Jiao, Can Chen
Summary: The paper studies the Bogdanov-Takens (B-T) bifurcation of a delayed predator-prey system with double Allee effect in prey. By analyzing the existence conditions of the B-T bifurcation, the associated generic unfolding and normal forms of the model at its interior equilibria are derived using the normal form theory and center manifold theorem for delay differential equations. The analysis of the topologically equivalent normal form system reveals that the Allee effect and delay can lead to various dynamic behaviors, providing insights into the potential mathematical mechanism driving population dynamics.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics
Yining Xie, Jing Zhao, Ruizhi Yang
Summary: This paper proposes a diffusive predator-prey model with a strong Allee effect and nonlocal competition in the prey and a fear effect and gestation delay in the predator. The study mainly focuses on the local stability of the coexisting equilibrium and the existence and properties of Hopf bifurcation. Bifurcation diagrams with the fear effect parameter (s) and the Allee effect parameter (a) are provided, showing that the stable region of the coexisting equilibrium increases (or decreases) with an increase in the fear effect parameter (s) (or the Allee effect parameter (a)). The results demonstrate that the fear effect parameter (s), the Allee effect parameter (a), and gestation delay (t) can be utilized to control the growth of prey and predator populations.
Article
Mathematics, Interdisciplinary Applications
Xiaoshuang Li, Danfeng Pang, Philip Wallhead, Richard Garth James Bellerby
Summary: This study investigates the impacts of ocean acidification and Allee effects on the dynamics of a marine predator-prey system. The study considers a diffusive predator-prey model with a double Allee effect on prey and a pH-dependent capture rate. The results show that changing environmental conditions can fundamentally alter the system dynamics, leading to decreased abundance and diversity of marine species by weakening predation rates. Additionally, the stability of periodic solutions is determined by double Allee effect parameters, with longer wavelengths observed as the Allee effect increases.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Zhimin Bi, Shutang Liu, Miao Ouyang
Summary: This paper investigates the spatial dynamics of a class of spatial fractional predator-prey systems with time delay and Allee effect. The conditions for Hopf bifurcation and Turing bifurcation are obtained, and the abundant dynamic behaviors of the system are demonstrated through numerical simulation. The numerical results show that time delay, Allee effect, and fractional diffusion can affect the formation of 3D Turing patterns and the constitution of 3D spiral wave patterns.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Physics, Multidisciplinary
Youwei Yang, Daiyong Wu, Chuansheng Shen, Fengping Lu
Summary: Nonlocal competition and Allee effect are studied in a predator-prey system, where the prey faces nonlocal competition and the predator is subject to Allee effect. The effects of predation on the spatial distribution of prey are investigated. The conditions for stable coexistence equilibrium, spatially inhomogeneous Hopf bifurcation, and Turing bifurcation are studied. Numerical simulations are carried out to illustrate the theoretical results, showing that nonlocal prey competition can destabilize the coexistence equilibrium point and drive spatially inhomogeneous bifurcations. The results also indicate that a larger habitat domain requires a larger prey diffusion coefficient for coexistence in the spatially homogeneous form.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Mathematics, Applied
Qing Yang, Xinhong Zhang, Daqing Jiang, Mingguang Shao
Summary: This paper investigates a stochastic predator-prey model with weak Allee effect and Holling-(n+1) functional response. Firstly, the existence of unique global positive solution to the model is verified, and the boundedness of the theta-th moment of the solution is studied. Secondly, the corresponding one-dimensional model is investigated, and the explicit density function of the solution is obtained. Then, a new technique is adopted to establish a sufficient and almost necessary condition for the existence of the unique ergodic stationary distribution and extinction based on the results of the one-dimensional system and a series of appropriate Lyapunov functions. Next, the dynamical behavior of the model with Markovian switching is analyzed and some main conclusions are derived. Finally, numerical simulations are conducted to illustrate the theoretical results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Materials Science, Multidisciplinary
Nursanti Anggriani, Hasan S. Panigoro, Emli Rahmi, Olumuyiwa James Peter, Sayooj Aby Jose
Summary: This study examines a mathematical model of prey-predator interaction, incorporating the additive Allee effect and intraspecific competition on the predator. The Atangana-Baleanu-Caputo fractional derivative (ABC) is utilized to account for the memory effect on the model's behavioral dynamics. The model's feasibility and validity are confirmed through the existence, uniqueness, non-negativity, and boundedness of the solution. Equilibrium points at the origin, axial, and interior are identified, with their conditions of existence determined. The stability condition for each equilibrium point is investigated using the Lyapunov direct method for the ABC model. Numerical simulations are conducted to demonstrate the impact of various biological parameters on the solution dynamics. The emergence of transcritical, saddle-node, and backward bifurcations driven by the Allee constant leads to the occurrence of bistability conditions, while a Hopf bifurcation and the evolution of a limit-cycle are observed due to the memory effect. The biological interpretation of each analytical and numerical result illustrates how the population densities of both species continuously balance in their ecosystem.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Li Ke, Li Shimin, Wu Kuilin
Summary: In this paper, the properties of a Leslie-Gower predator-prey system are investigated under two basic assumptions. The results show that the system exhibits rich dynamics, including subcritical Hopf bifurcation, canard explosion, and relaxation oscillations. Numerical simulations are conducted to validate the analytical findings.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Applied
Aytul Gokce
Summary: This paper investigates the effects of constant time delays on a population dynamics model with Allee effect and weakening memory. Analytical and numerical analyses are conducted to study the role of delays in competition and cooperation. The results demonstrate that time delays can significantly impact the system behavior and offer important insights into underlying biological mechanisms.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematical & Computational Biology
Jia Liu
Summary: This study investigates a diffusive predator-prey model with multiple Allee effects induced by fear factors, examining the existence, boundedness, and permanence of solutions as well as discussing the possibility of non-constant solutions. It also derives conditions for homogeneous and non-homogeneous bifurcations. Theoretical and numerical simulations demonstrate the significant impact of strong Allee effect and fear effect on the system dynamics.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2021)
Article
Mathematics
Meng Zhu, Jing Li, Xinze Lian
Summary: This paper investigates a Leslie-Gower cross diffusion predator-prey model with a strong Allee effect and hunting cooperation. The effects of self diffusion and cross diffusion on the stability of the homogeneous state point and processes of pattern formation are mainly studied. The research shows that self diffusion and cross diffusion have important effects on the formation of spatial patterns.
Article
Mathematics, Applied
Yuying Liu, Junjie Wei
Summary: This paper studies a diffusive predator-prey system with strong Allee effect and two delays. Stability analysis, Hopf and double Hopf bifurcation theorems, and numerical simulations are used to explore the system's dynamics near double Hopf singularity, showing rich dynamics including stable periodic solutions. The influence of two parameters on the existence of double Hopf bifurcation is evaluated.
NONLINEAR ANALYSIS-MODELLING AND CONTROL
(2021)
Article
Mathematics, Interdisciplinary Applications
Shuangte Wang, Hengguo Yu
Summary: This paper studies the complex dynamical behaviors of a predator-prey system with the Beddington-DeAngelis functional response and the Allee-like effect on predator through qualitative analysis and numerical simulations. Theoretical derivations provide conditions for various bifurcations, which are verified by computer simulations. This work aims to establish a theoretical basis for future research on complexity in predator-prey ecosystems.
DISCRETE DYNAMICS IN NATURE AND SOCIETY
(2021)
Article
Mathematical & Computational Biology
Sangeeta Saha, Guruprasad Samanta
Summary: In an environment, predators can switch between different prey populations to increase their overall growth rate. This study proposes a system with two prey populations and one predator, where the predator exhibits switching behavior between the prey species. The system is well-defined and the stability analysis shows the existence of stable and unstable equilibrium points.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2023)
Article
Mathematical & Computational Biology
Haixia Li, Wenbin Yang, Meihua Wei, Aili Wang
Summary: This paper investigates a diffusive modified Leslie-Gower predator-prey system with double Allee effect on prey, determining the global existence, uniqueness, and a priori bound of positive solutions. It also analyzes the existence and local stability of constant steady-state solutions, as well as the nonexistence of nonconstant positive steady-state solutions. The study further discusses steady-state bifurcation, existence of nonconstant positive steady-state solutions, and Hopf bifurcations of spatially homogeneous and inhomogeneous periodic orbits.
INTERNATIONAL JOURNAL OF BIOMATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)