Article
Mathematics, Interdisciplinary Applications
Qingyan Shi, Yongli Song
Summary: The dynamics of a pollen tube model with nonlocal effect and time delay are investigated in this paper. Compared to the model without delay, a double Hopf bifurcation occurs due to the interaction of homogeneous and nonhomogeneous Hopf bifurcations, leading to the observation of quasi periodic patterns. Additionally, the interaction of Turing bifurcation and spatially nonhomogeneous Hopf bifurcation results in new spatiotemporal patterns.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Ruizhi Yang, Chenxuan Nie, Dan Jin
Summary: This paper investigates a delayed diffusive predator-prey model with nonlocal competition and habitat complexity. The local stability of coexisting equilibrium is studied by analyzing the eigenvalue spectrum. Time delay inducing Hopf bifurcation is explored using time delay as a bifurcation parameter. Conditions for determining the bifurcation direction and stability of the bifurcating periodic solution are derived using the normal form method and center manifold theorem. The results suggest that only the combination of nonlocal competition and diffusion can induce stably spatial inhomogeneous bifurcating periodic solutions.
NONLINEAR DYNAMICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Shangjiang Guo, Shangzhi Li, Bounsanong Sounvoravong
Summary: This paper investigates a reaction-diffusion model with delay effect and Dirichlet boundary condition, obtaining the existence and patterns of spatially nonhomogeneous steady-state solutions through Lyapunov-Schmidt reduction. Furthermore, the stability conditions of nontrivial synchronous steady-state solutions are discussed, along with the effect of time delay on pattern formation. The study also explores the spontaneous bifurcation of multiple branches of nonlinear wave solutions and their spatiotemporal patterns using symmetric bifurcation theory and representation theory of standard dihedral groups.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematics, Applied
Liye Wang, Wenlong Wang, Ruizhi Yang
Summary: This paper studies the effect of nonlocal competition term in a plankton model with toxic substances. The stability of the positive equilibrium point and the existence of Hopf bifurcations are discussed by analyzing the distribution of eigenvalues. The direction and stability of bifurcation periodic solution are researched based on an extended central manifold method and normal theory. Finally, spatially inhomogeneous oscillations are observed in the vicinity of the Hopf bifurcations.
Article
Mathematics, Applied
Chenxuan Nie, Dan Jin, Ruizhi Yang
Summary: This study considers a delayed diffusive predator-prey system with nonlocal competition and generalist predators. The local stability of the positive equilibrium and Hopf bifurcation at positive equilibrium is investigated using time delay as a parameter. Additionally, the properties of Hopf bifurcation are analyzed using the center manifold theorem and normal form method. It is found that time delays can influence the stability of the positive equilibrium and induce spatially inhomogeneous periodic oscillation of prey and predator population densities.
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
Shangjiang Guo
Summary: This study investigates the existence, stability, and multiplicity of steady-state solutions and periodic solutions for a reaction-diffusion model with nonlocal delay effect and nonlinear boundary condition using Lyapunov-Schmidt reduction. It is found that when the interior reaction term is weaker than the boundary reaction term, there is no Hopf bifurcation, while if the interior reaction term is stronger, the existence of Hopf bifurcation depends on the interior reaction delay. The general results are illustrated by applying models with either a single delay or bistable boundary condition.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Wen Wang, Shutang Liu
Summary: This paper presents the Turing-Hopf bifurcation analysis and resulting spatiotemporal dynamics in a single-species reaction-diffusion model with nonlocal delay. Linear stability analysis is used to determine the conditions for Turing-Hopf bifurcation, and weakly nonlinear analysis is employed to derive the amplitude equations for the slow-time evolution of critical modes. The use of amplitude equations allows for the determination of stability conditions and prediction of spatiotemporal patterns near the bifurcation point. Numerical simulations are conducted to verify the theoretical results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Chunyan Gao, Fangqi Chen
Summary: This study developed a general model of delayed p53 regulatory network in DNA damage response by introducing microRNA 192-mediated positive feedback loop. It was found that time delay can drive p53 oscillation and miR-192 affects the stability of system oscillations.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2021)
Article
Mathematics
Zhucheng Jin, Rong Yuan
Summary: This paper investigates the dynamics of a general reaction-diffusion-advection equation with nonlocal delay effect and Dirichlet boundary condition. The existence of positive spatially nonhomogeneous steady state solution is shown, with proof of Hopf bifurcation by analyzing the distribution of eigenvalues. Weighted space is introduced to overcome the hurdle from advection term, and the effect of adding a term advection along environmental gradients to Hopf bifurcation value for a Logistic equation with nonlocal delay is demonstrated.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Shuhao Wu, Yongli Song, Qingyan Shi
Summary: This paper discusses a reaction-diffusion model incorporating delay and nonlocal effects. The normal form of double Hopf bifurcation is derived. The diffusive model of pollen tube tip growth is examined and numerical simulations demonstrate that spatially homogeneous and inhomogeneous periodic solutions can be stable or connected by a heteroclinic orbit under certain conditions. Additionally, the diffusive Lotka-Volterra model with delay and nonlocality is considered and a spatially inhomogeneous quasi-periodic solution is obtained.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Biology
Tak Fung, Hannah E. Clapham, Ryan A. Chisholm
Summary: Many infectious diseases, including dengue, have multiple variants, and the interactions between these variants may drive epidemiological dynamics. This study analyzes the importance of temporary cross-immunity (TCI) and antibody-dependent enhancement (ADE) in cyclic outbreaks of dengue serotypes. The presence of TCI allows asynchronous cycles of serotypes, while ADE enhances transmission rates.
BULLETIN OF MATHEMATICAL BIOLOGY
(2023)
Article
Mathematics, Applied
Yanqiu Li, Yibo Zhou, Lushuai Zhu
Summary: A spatial heterogeneous and nonlocal delayed reaction-diffusion equation is studied. The existence of nontrivial steady-state solution is demonstrated through steady-state bifurcation at the trivial solution. The form of the positive spatially nonhomogeneous steady state is provided under certain conditions. Based on this form, the stability and Hopf bifurcation are analyzed, thereby showing the periodic and quasi-periodic solutions near the spatially nonhomogeneous steady state.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics, Applied
Q. I. N. G. Y. A. N. Shi, Y. O. N. G. L. Song
Summary: This paper proposes a diffusive model with nonlocal memory-based diffusion to model animal movement. The stability of the positive homogeneous steady state and the bifurcation behaviors are investigated by taking the memory delay and the memory-based diffusion coefficient as bifurcation parameters. Rich dynamics in the system are observed, including Turing bifurcations and Hopf bifurcations.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematics, Applied
Tingting Wen, Xiaoli Wang, Guohong Zhang
Summary: We investigate a reaction-diffusion-advection logistic model with two nonlocal delayed density-dependent terms and zero-Dirichlet boundary conditions. The existence of positive non-homogeneous steady states and the associated Hopf bifurcation are proven. The influence of advection on Hopf bifurcation and stability switches is examined, and it is found that the critical values of the bifurcation parameter increase (decrease) with the increase of advection rate in a positive (negative) range, indicating that the advective effect decelerates (accelerates) the generation of Hopf bifurcation to some extent if the advection rate lies in a certain positive (negative) range. (c) 2023 Elsevier B.V. All rights reserved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Biology
Andreas Buttenschon, Thomas Hillen, Alf Gerisch, Kevin J. Painter
JOURNAL OF MATHEMATICAL BIOLOGY
(2018)
Article
Ecology
Andrew W. Bateman, Andreas Buttenschon, Kelley D. Erickson, Nathan G. } Marculis
THEORETICAL ECOLOGY
(2017)
Article
Biology
Andreas Buttenschon, Leah Edelstein-Keshet
JOURNAL OF MATHEMATICAL BIOLOGY
(2019)
Article
Biology
Andreas Buttenschon, Yue Liu, Leah Edelstein-Keshet
BULLETIN OF MATHEMATICAL BIOLOGY
(2020)
Article
Mathematics, Applied
Thomas Hillen, Andreas Buttenschon
SIAM JOURNAL ON APPLIED MATHEMATICS
(2020)
Review
Biochemical Research Methods
Andreas Buttenschon, Leah Edelstein-Keshet
PLOS COMPUTATIONAL BIOLOGY
(2020)
Article
Biology
Andreas Buttenschon, Leah Edelstein-Keshet
Summary: The intrinsic polarity of migrating cells is regulated by spatial distributions of protein activity. This process can be explained by reaction-diffusion equations. The article numerically simulated and analyzed two polarity models, finding distinct routes to repolarization and consistent results with biological experiments.
BULLETIN OF MATHEMATICAL BIOLOGY
(2022)