Multiple limit cycles in a Gause type predator-prey model with Holling type III functional response and Allee effect on prey.

Abstract:

:This work aims to examine the global behavior of a Gause type predator-prey model considering two aspects: (i) the functional response is Holling type III and, (ii) the prey growth is affected by the Allee effect. We prove the origin of the system is an attractor equilibrium point for all parameter values. It has also been shown that it is the ω-limit of a wide set of trajectories of the system, due to the existence of a separatrix curve determined by the stable manifold of the equilibrium point (m,0), which is associated to the Allee effect on prey. When a weak Allee effect on the prey is assumed, an important result is obtained, involving the existence of two limit cycles surrounding a unique positive equilibrium point: the innermost cycle is unstable and the outermost stable. This property, not yet reported in models considering a sigmoid functional response, is an important aspect for ecologists to acknowledge as regards the kind of tristability shown here: (1) the origin; (2) an interior equilibrium; and (3) a limit cycle of large amplitude. These models have undoubtedly been rather sensitive to disturbances and require careful management in applied conservation and renewable resource contexts.

journal_name

Bull Math Biol

authors

González-Olivares E,Rojas-Palma A

doi

10.1007/s11538-010-9577-5

subject

Has Abstract

pub_date

2011-06-01 00:00:00

pages

1378-97

issue

6

eissn

0092-8240

issn

1522-9602

journal_volume

73

pub_type

杂志文章
  • A within-host virus model with periodic multidrug therapy.

    abstract::This paper is devoted to the investigation of the effects of periodic drug treatment on a standard within-host virus model. We first introduce the basic reproduction ratio for the model, and then show that the infection free equilibrium is globally asymptotically stable, and the disease eventually disappears if R0<1, ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-013-9820-y

    authors: Wang Z,Zhao XQ

    更新日期:2013-03-01 00:00:00

  • Culture analysis and external interaction models of mycelial growth.

    abstract::To investigate morphogenesis and in particular circularization mechanisms in young mycelia, we observe cultures of the zygomycete Mucor spinosus and develop discrete models of two-dimensional filamental branching growth. The models are based on the hypothesis that the fungus secretes a regulatory substance that diffus...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02460715

    authors: Indermitte C,Liebling M,Clémençon H

    更新日期:1994-07-01 00:00:00

  • Tubuloglomerular feedback signal transduction in a short loop of henle.

    abstract::In previous studies, we used a mathematical model of the thick ascending limb (TAL) to investigate nonlinearities in the tubuloglomerular feedback (TGF) loop. That model does not represent other segments of the nephron, the water, and NaCl transport along which may impact fluid flow rate and NaCl transport along the T...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-009-9436-4

    authors: Layton AT,Edwards A

    更新日期:2010-01-01 00:00:00

  • On cloning and clone libraries for finite and infinite length genomes.

    abstract::This paper develops mathematical theory to determine the representativeness of clone libraries for various models, defined below in the text. In particular, the means and variances of fragment lengths and the mean of the length of a randomly selected fragment are determined, as well as the probability of the event tha...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1006/bulm.2001.0251

    authors: Fang Y,Wilson SR

    更新日期:2001-09-01 00:00:00

  • A phase-field model for articular cartilage regeneration in degradable scaffolds.

    abstract::Degradable scaffolds represent a promising solution for tissue engineering of damaged or degenerated articular cartilage which due to its avascular nature, is characterized by a low self-repair capacity. To estimate the articular cartilage regeneration process employing degradable scaffolds, we propose a mathematical ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-013-9897-3

    authors: Yun A,Lee SH,Kim J

    更新日期:2013-12-01 00:00:00

  • Regular Simple Queues of Protein Contact Maps.

    abstract::A protein fold can be viewed as a self-avoiding walk in certain lattice model, and its contact map is a graph that represents the patterns of contacts in the fold. Goldman, Istrail, and Papadimitriou showed that a contact map in the 2D square lattice can be decomposed into at most two stacks and one queue. In the term...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-016-0212-y

    authors: Guo QH,Sun LH,Wang J

    更新日期:2017-01-01 00:00:00

  • On the fractal geometry of DNA by the binary image analysis.

    abstract::The multifractal analysis of binary images of DNA is studied in order to define a methodological approach to the classification of DNA sequences. This method is based on the computation of some multifractality parameters on a suitable binary image of DNA, which takes into account the nucleotide distribution. The binar...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-013-9859-9

    authors: Cattani C,Pierro G

    更新日期:2013-09-01 00:00:00

  • Behavioural interactions selecting for symmetry and asymmetry in sexual reproductive systems of eusocial species.

    abstract::Understanding the life-history complex of eusociality has remained an enduring problem in evolutionary ecology, partially because natural selection models have considered traits in relative isolation. I aim for a more inclusive model that uses ecological interactions to predict the evolutionary existence of sexual rep...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-006-9112-x

    authors: Witting L

    更新日期:2007-05-01 00:00:00

  • On Nonlinear Pest/Vector Control via the Sterile Insect Technique: Impact of Residual Fertility.

    abstract::We consider a minimalist model for the Sterile Insect Technique (SIT), assuming that residual fertility can occur in the sterile male population. Taking into account that we are able to get regular measurements from the biological system along the control duration, such as the size of the wild insect population, we st...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00790-3

    authors: Aronna MS,Dumont Y

    更新日期:2020-08-09 00:00:00

  • A general formulation of the concept of independent action for the combined effects of agents.

    abstract::Analysis schemes for the classification of synergism and antagonism for mixed agents operate on the discrepancies between observed and calculated results. As such they cannot be confirmed by experiments and therefore have to be tested in terms of mathematical and logical self-consistency. The concept of independent ac...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02458276

    authors: Lam GK

    更新日期:1994-09-01 00:00:00

  • Analysis of a vector-bias model on malaria transmission.

    abstract::We incorporate a vector-bias term into a malaria-transmission model to account for the greater attractiveness of infectious humans to mosquitoes in terms of differing probabilities that a mosquito arriving at a human at random picks that human depending on whether he is infectious or susceptible. We prove that transcr...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-010-9545-0

    authors: Chamchod F,Britton NF

    更新日期:2011-03-01 00:00:00

  • The Effects of Insulin Resistance on Individual Tissues: An Application of a Mathematical Model of Metabolism in Humans.

    abstract::Whilst the human body expends energy constantly, the human diet consists of a mix of carbohydrates and fats delivered in a discontinuous manner. To deal with this sporadic supply of energy, there are transport, storage and utilisation mechanisms, for both carbohydrates and fats, around all tissues of the body. Insulin...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-016-0181-1

    authors: Pearson T,Wattis JA,King JR,MacDonald IA,Mazzatti DJ

    更新日期:2016-06-01 00:00:00

  • Bistability, oscillations, and traveling waves in frog egg extracts.

    abstract::Mathematical modeling is a powerful tool for unraveling the complexities of the molecular regulatory networks underlying all aspects of cell physiology. To support this claim, we review our experiences modeling the cyclin-dependent kinase (CDK) network that controls events of the eukaryotic cell cycle. The model was d...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-014-0009-9

    authors: Tyson JJ,Novak B

    更新日期:2015-05-01 00:00:00

  • Are Tumor Cell Lineages Solely Shaped by Mechanical Forces?

    abstract::This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM m...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-017-0333-y

    authors: Leroy-Lerêtre M,Dimarco G,Cazales M,Boizeau ML,Ducommun B,Lobjois V,Degond P

    更新日期:2017-10-01 00:00:00

  • Dicarboxylic acid fluxes during gluconeogenesis. No channelling of mitochondrial oxalacetate.

    abstract::A rather complete model of the gluconeogenic pathway was used, with the known separate pools of mitochondrial and cytosolic oxalacetate, malate and aspartate. The fumarase, malate dehydrogenase and glutamate oxalacetate transaminase reactions were assumed to be isotopically actively reversible, but none at isotopic eq...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02460783

    authors: Rognstad R

    更新日期:1995-07-01 00:00:00

  • Analyzing the fitch method for reconstructing ancestral states on ultrametric phylogenetic trees.

    abstract::The accuracy of the Fitch method for reconstructing ancestral states on ultrametric phylogenetic trees is studied. Two recurrence relations for computing the accuracy are given here. Using these relations, we analyze the convergence of the accuracy of the Fitch method for reconstructing the root state on a complete bi...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-010-9505-8

    authors: Zhang L,Shen J,Yang J,Li G

    更新日期:2010-10-01 00:00:00

  • A Metaecoepidemic Model of Grassland Ecosystem with Only Consumers' Migration.

    abstract::Metaecoepidemic models generalize metapopulation systems, combining local population dynamics with inter-patch migration coupled with an epidemic proliferation. A resource-consumer model is introduced with an ecosystem composed by two patches, in which consumers can freely move. A disease affects resources of the seco...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-020-00764-5

    authors: Moulin T,Perasso A,Venturino E

    更新日期:2020-07-07 00:00:00

  • Times from Infection to Disease-Induced Death and their Influence on Final Population Sizes After Epidemic Outbreaks.

    abstract::For epidemic models, it is shown that fatal infectious diseases cannot drive the host population into extinction if the incidence function is upper density-dependent. This finding holds even if a latency period is included and the time from infection to disease-induced death has an arbitrary length distribution. Howev...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-0446-y

    authors: Farrell AP,Collins JP,Greer AL,Thieme HR

    更新日期:2018-07-01 00:00:00

  • Modeling the Role of Feedback in the Adaptive Response of Bacterial Quorum Sensing.

    abstract::Bacterial quorum sensing (QS) is a form of intercellular communication that relies on the production and detection of diffusive signaling molecules called autoinducers. Such a mechanism allows the bacteria to track their cell density in order to regulate group behavior, such as biofilm formation and bioluminescence. I...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00570-8

    authors: Fan G,Bressloff PC

    更新日期:2019-05-01 00:00:00

  • Catch Me If You Can: A Spatial Model for a Brake-Driven Gene Drive Reversal.

    abstract::Population management using artificial gene drives (alleles biasing inheritance, increasing their own transmission to offspring) is becoming a realistic possibility with the development of CRISPR-Cas genetic engineering. A gene drive may, however, have to be stopped. "Antidotes" (brakes) have been suggested, but have ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00668-z

    authors: Girardin L,Calvez V,Débarre F

    更新日期:2019-12-01 00:00:00

  • An algebraic-combinatorial model for the identification and mapping of biochemical pathways.

    abstract::We develop the mathematical machinery for the construction of an algebraic-combinatorial model using Petri nets to construct an oriented matroid representation of biochemical pathways. For demonstration purposes, we use a model metabolic pathway example from the literature to derive a general biochemical reaction netw...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1006/bulm.2001.0263

    authors: Oliveira JS,Bailey CG,Jones-Oliveira JB,Dixon DA

    更新日期:2001-11-01 00:00:00

  • Mutation and Selection in Bacteria: Modelling and Calibration.

    abstract::Temporal evolution of a clonal bacterial population is modelled taking into account reversible mutation and selection mechanisms. For the mutation model, an efficient algorithm is proposed to verify whether experimental data can be explained by this model. The selection-mutation model has unobservable fitness paramete...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-018-0529-9

    authors: Bayliss CD,Fallaize C,Howitt R,Tretyakov MV

    更新日期:2019-03-01 00:00:00

  • A new model for laser-induced thermal damage in the retina.

    abstract::We describe a new model for laser-induced retinal damage. Our treatment is prompted by the failure of the traditional approach to accurately describe the image size dependence of laser-induced retinal injuries and by a recently reported study which demonstrated that laser injuries to the retina might not appear for up...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1016/S0092-8240(03)00028-4

    authors: Till SJ,Till J,Milsom PK,Rowlands G

    更新日期:2003-07-01 00:00:00

  • Network development in biological gels: role in lymphatic vessel development.

    abstract::In this paper, we present a model that explains the prepatterning of lymphatic vessel morphology in collagen gels. This model is derived using the theory of two phase rubber material due to Flory and coworkers and it consists of two coupled fourth order partial differential equations describing the evolution of the co...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-008-9324-3

    authors: Roose T,Fowler AC

    更新日期:2008-08-01 00:00:00

  • Predicting Pattern Formation in Multilayer Networks.

    abstract::We investigate how the structure of interactions between coupled oscillators influences the formation of asynchronous patterns in a multilayer network by formulating a simple, general multilayer oscillator model. We demonstrate the analysis of this model in three-oscillator systems, illustrating the role of interactio...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00682-1

    authors: Hayes SM,Anderson KE

    更新日期:2019-12-20 00:00:00

  • A mathematical model for fibro-proliferative wound healing disorders.

    abstract::The normal process of dermal wound healing fails in some cases, due to fibro-proliferative disorders such as keloid and hypertrophic scars. These types of abnormal healing may be regarded as pathologically excessive responses to wounding in terms of fibroblastic cell profiles and their inflammatory growth-factor media...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/BF02459482

    authors: Olsen L,Sherratt JA,Maini PK

    更新日期:1996-07-01 00:00:00

  • A Diffusion Approximation Based on Renewal Processes with Applications to Strongly Biased Run-Tumble Motion.

    abstract::We consider organisms which use a renewal strategy such as run-tumble when moving in space, for example to perform chemotaxis in chemical gradients. We derive a diffusion approximation for the motion, applying a central limit theorem due to Anscombe for renewal-reward processes; this theorem has not previously been ap...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-016-0155-3

    authors: Thygesen UH

    更新日期:2016-03-01 00:00:00

  • Mathematical models for the Aedes aegypti dispersal dynamics: travelling waves by wing and wind.

    abstract::Biological invasion is an important area of research in mathematical biology and more so if it concerns species which are vectors for diseases threatening the public health of large populations. That is certainly the case for Aedes aegypti and the dengue epidemics in South America. Without the prospect of an effective...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1016/j.bulm.2004.08.005

    authors: Takahashi LT,Maidana NA,Ferreira WC Jr,Pulino P,Yang HM

    更新日期:2005-05-01 00:00:00

  • A geometric buildup algorithm for the solution of the distance geometry problem using least-squares approximation.

    abstract::We propose a new geometric buildup algorithm for the solution of the distance geometry problem in protein modeling, which can prevent the accumulation of the rounding errors in the buildup calculations successfully and also tolerate small errors in given distances. In this algorithm, we use all instead of a subset of ...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-009-9431-9

    authors: Sit A,Wu Z,Yuan Y

    更新日期:2009-11-01 00:00:00

  • A Population Dynamics Model of Mosquito-Borne Disease Transmission, Focusing on Mosquitoes' Biased Distribution and Mosquito Repellent Use.

    abstract::We present an improved mathematical model of population dynamics of mosquito-borne disease transmission. Our model considers the effect of mosquito repellent use and the mosquito's behavior or attraction to the infected human, which cause mosquitoes' biased distribution around the human population. Our analysis of the...

    journal_title:Bulletin of mathematical biology

    pub_type: 杂志文章

    doi:10.1007/s11538-019-00666-1

    authors: Aldila D,Seno H

    更新日期:2019-12-01 00:00:00