# Competitive Exclusion in a Discrete Stage-Structured Two Species Model

Mathematical Modelling of Natural Phenomena (2009)

- Volume: 4, Issue: 6, page 156-175
- ISSN: 0973-5348

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topAckleh, A. S., and Zhang, P.. "Competitive Exclusion in a Discrete Stage-Structured Two Species Model." Mathematical Modelling of Natural Phenomena 4.6 (2009): 156-175. <http://eudml.org/doc/222295>.

@article{Ackleh2009,

abstract = {
We develop a stage-structured model that
describes the dynamics of two competing species each of which have sexual
and clonal reproduction. This is typical of many plants including irises.
We first analyze the dynamical behavior of a single species model. We show
that when the inherent net reproductive number is smaller than one then the
population will go to extinction and if it is larger than one then
an interior equilibrium exists and it is globally asymptotically
stable. Then we analyze the two-species model and establish
conditions on the reproduction and survivorship rates that lead to competitive exclusion. We show that
the winner species is the one that attains higher density at which its net reproductive number equals unity.
Numerical results corroborating the theoretical ones are also presented.
},

author = {Ackleh, A. S., Zhang, P.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {stage-structured model; net
reproductive number; competitive exclusion; net reproductive number},

language = {eng},

month = {11},

number = {6},

pages = {156-175},

publisher = {EDP Sciences},

title = {Competitive Exclusion in a Discrete Stage-Structured Two Species Model},

url = {http://eudml.org/doc/222295},

volume = {4},

year = {2009},

}

TY - JOUR

AU - Ackleh, A. S.

AU - Zhang, P.

TI - Competitive Exclusion in a Discrete Stage-Structured Two Species Model

JO - Mathematical Modelling of Natural Phenomena

DA - 2009/11//

PB - EDP Sciences

VL - 4

IS - 6

SP - 156

EP - 175

AB -
We develop a stage-structured model that
describes the dynamics of two competing species each of which have sexual
and clonal reproduction. This is typical of many plants including irises.
We first analyze the dynamical behavior of a single species model. We show
that when the inherent net reproductive number is smaller than one then the
population will go to extinction and if it is larger than one then
an interior equilibrium exists and it is globally asymptotically
stable. Then we analyze the two-species model and establish
conditions on the reproduction and survivorship rates that lead to competitive exclusion. We show that
the winner species is the one that attains higher density at which its net reproductive number equals unity.
Numerical results corroborating the theoretical ones are also presented.

LA - eng

KW - stage-structured model; net
reproductive number; competitive exclusion; net reproductive number

UR - http://eudml.org/doc/222295

ER -

## References

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