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Stability and Hopf bifurcation in a prey-predator model with memory-based diffusion
2022
Discrete and continuous dynamical systems. Series B
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<p style='text-indent:20px;'>In this paper, we consider a predator-prey model with memory-based diffusion. We first analyze the stability of all steady states in detail. ...
Moreover, from the central manifold theorem and the normal form theory, we give the direction and stability of Hopf bifurcation. ...
We sincerely thank the anonymous referees for the careful reading and valuable comments which led to improvements of our original manuscript. ...
doi:10.3934/dcdsb.2022025
fatcat:yf37eguybbd7dnfv6jqpon4dtm
Chemotactic Signaling, Microglia, and Alzheimer's Disease Senile Plaques: Is There a Connection?
2003
Bulletin of Mathematical Biology
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We develop a model for chemotaxis in response to a combination of chemoattractant and chemorepellent signaling chemicals. ...
Linear stability analysis and numerical simulations of the model predict that periodic patterns in cell and chemical distributions can evolve under local attraction, longranged repulsion, and other constraints ...
ACKNOWLEDGEMENTS ML, LEK, and ACR were supported by the Mathematics of Information Technology and Complex Systems (MITACS) under the Networks of Centers of Excellence program (Canada), and by a NSERC ( ...
doi:10.1016/s0092-8240(03)00030-2
pmid:12875339
fatcat:xiq77sjbibfajm5cm45763jmbq
Dynamics of a memory-based diffusion model with spatial heterogeneity and nonlinear boundary condition
[article]
2024
arXiv
pre-print
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Therefore, the memory delay will lead to a single stability switch of such memory-based diffusive model and consequently the Hopf bifurcation will happen in the model. ...
In this work, we study the dynamics of a spatially heterogeneous single population model with the memory effect and nonlinear boundary condition. ...
[12] investigated the memory-based diffusion model (1) with nonlocal effect in reaction term, which showed that the emergence of Turing-Hopf and double Hopf bifurcations could be induced by the joint ...
arXiv:2403.14969v1
fatcat:adbosktburdjzp3kytphntbh4y
Spatiotemporal mutualistic model of mistletoes and birds
2013
Journal of Mathematical Biology
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Fickian diffusion and chemotaxis are used to model the random movement of birds and the aggregation of birds due to the attraction of mistletoes, respectively. ...
A mathematical model which incorporates the spatial dispersal and interaction dynamics of mistletoes and birds is derived and studied to gain insights of the spatial heterogeneity in abundance of mistletoes ...
Acknowledgments We are grateful to the anonymous referees for their constructive and helpful comments to improve this work. We thank Professors Mark Lewis and Yuan Lou for some helpful suggestions. ...
doi:10.1007/s00285-013-0664-8
pmid:23604589
fatcat:4h4q37asqrcfdedxooq6xw5a7y
Analysis of a spatial memory model with nonlocal maturation delay and hostile boundary condition
2020
Discrete and Continuous Dynamical Systems. Series A
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In this paper, we propose and investigate a memory-based reactiondiffusion equation with nonlocal maturation delay and homogeneous Dirichlet boundary condition. ...
The bifurcation analysis reveals that the diffusion with memory effect could induce spatiotemporal patterns which were never possessed by an equation without memory-based diffusion. ...
In fact, the models with nonlocal reaction terms are more realistic than those with local ones. ...
doi:10.3934/dcds.2020249
fatcat:uof6k2yjsrh5bkcnes7osooj5y
Interaction between water and plants: Rich dynamics in a simple model
2017
Discrete and continuous dynamical systems. Series B
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Hopf bifurcations, bubble loop of limit cycles, homoclinic bifurcation and Bogdanov-Takens bifurcation. ...
An ordinary differential equation model describing interaction of water and plants in ecosystem is proposed. ...
The authors wish to express their grateful thanks to the anonymous referees for their careful reading and some valuable comments and suggestions which greatly improved this work. ...
doi:10.3934/dcdsb.2017159
fatcat:6a6hfcusifhongbqenf4zp4dau
Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping
[article]
2023
arXiv
pre-print
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Most generally, these models take the form of nonlocal reaction-diffusion-advection equations, where the nonlocality may appear in the spatial domain, the temporal domain, or both. ...
Mathematical rules of thumb are provided to judge the model rationality, to aid in model development or interpretation, and to streamline an understanding of the range of difficulty in possible model conceptions ...
on reaction-advection-diffusion equations. ...
arXiv:2201.09150v3
fatcat:waqrecymnfemroogog6gwqkslu
Regularity, Asymptotic Solutions and Travelling Waves Analysis in a Porous Medium System to Model the Interaction between Invasive and Invaded Species
2022
Mathematics
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a TW trajectory governed by the invaded species runaway (in the direction of the advection) and the diffusion (acting in a finite speed front or support). ...
The finding of an exponential decaying rate (related with the advection and diffusion parameters) in the invaded species TW is not trivial in the nonlinear diffusion case and reflects the existence of ...
Similar stability and bifurcation methods have been used in [9] for a predator-prey model subject to the Allee effect with a discrete-time Holling type-IV functional response. ...
doi:10.3390/math10071186
fatcat:sxujegja65hqbph5lxctohruhu
Nonlocal Models in Biology and Life Sciences: Sources, Developments, and Applications
[article]
2024
arXiv
pre-print
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Additionally, we have reviewed a nonlocal theory of peridynamics, which deals with continuous and discrete media and applies to model the relationship between fracture and healing in cortical bone, tissue ...
In addition, we have discussed nonlocal modelling approaches for cancer stem cells and tumor cells that are widely applied in the cell migration processes, growth, and avascular tumors in any organ. ...
accreditation SEV-2017-0718 and the Basque Government fund AI in BCAM EXP. 2019/00432. ...
arXiv:2401.14651v1
fatcat:dxm4ky6xgzeuvhm6x7nfvd5ciy
Pattern formation in a nonlocal mathematical model for the multiple roles of the TGF- β pathway in tumour dynamics
2017
Mathematical Biosciences
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by reaction-diffusion equations, and the growth
47 and movement of the tumour was described by a particle-based model). ...
We then couple
65 this system with a local reaction-diffusion equation for the dynamics of TGF-β
66 molecules. ...
doi:10.1016/j.mbs.2017.05.003
pmid:28511959
fatcat:utrbxozx3rhfvgph54g55gylna
Existence, Stability, and Dynamics of Ring and Near-Ring Solutions to the Saturated Gierer--Meinhardt Model in the Semistrong Regime
2017
SIAM Journal on Applied Dynamical Systems
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We analyze a singularly perturbed reaction-diffusion system in the semi-strong diffusion regime in two spatial dimensions where an activator species is localized to a closed curve, while the inhibitor ...
A detailed analysis of the existence, stability, and dynamics of ring and near-ring solutions for the GMS model is given, whereby the activator concentrates on a thin ring concentric within a circular ...
In (1.1), τ is an effective time scale delay between the activator and inhibitor, while D and 2 , with 1, are the inhibitor and activator diffusivities respectively. ...
doi:10.1137/16m1060327
fatcat:hxoqtzsb6nbm3h4ecqqgnaczde
Existence, Stability and Slow Dynamics of Spikes in a 1D Minimal Keller–Segel Model with Logistic Growth
[article]
2023
arXiv
pre-print
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We analyze the existence, linear stability, and slow dynamics of localized 1D spike patterns for a Keller–Segel model of chemotaxis that includes the effect of logistic growth of the cellular population ...
if the cellular diffusion rate d_1 exceeds a threshold, or from a Hopf bifurcation if a relaxation time constant τ is too large. ...
Kolokolnikov for useful discussions and many critical suggestions. The research of M.J. Ward and J. Wei is partially supported by NSERC of Canada. ...
arXiv:2307.15896v1
fatcat:7msgki43yzfbzc7lb3a7gxnk2u
Page 710 of Mathematical Reviews Vol. , Issue Index
[page]
Mathematical Reviews
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A., 97b:92024
Busenberg, Stavros (with Huang, Wenzhang) Stability and Hopf bifurcation for a population delay model with diffusion effects. 97b:35179
Busoni, Giorgio (with Matucci, S.) ...
Stability and bifurcation in delay diffusion models. (English summary) 97g:92012
Choudhury, Sudipto Roy (with Fosser,C.) Turing bifurcation in nonlinear competition models with delay. ...
Page 889 of Mathematical Reviews Vol. , Issue Subject Index
[page]
Mathematical Reviews
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, 2001a:92040 and Smith, Hal L., 2001¢:35239
Zhou, Li' (with Fu, Yiping) Stability and Hopf bifurcation of stationary solution of a delay equation. ...
(with Zhao, Xiao-Qiang) Global asymptotic stability of traveling waves in delayed reaction-diffusion equations. ...
Page 944 of Mathematical Reviews Vol. , Issue Subject Index
[page]
Mathematical Reviews
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in diffusive ecological models with nonlocal delay effects. ...
(English, French and Arabic summaries 2002k:35162
Amraoui, Saida (with Lalaoui Rhali, Soumia) Hopf bifurcation for a diffusion model with several delays. ...
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