ORGANISATION/COMPANYUniversité Clermont Auvergne
RESEARCHER PROFILEFirst Stage Researcher (R1)
APPLICATION DEADLINE21/05/2020 23:00 - Europe/Brussels
LOCATIONFrance › AUBIERE
TYPE OF CONTRACTOther
HOURS PER WEEK35 H
OFFER STARTING DATE01/10/2020
IS THE JOB RELATED TO STAFF POSITION WITHIN A RESEARCH INFRASTRUCTURE?Yes
Title of the thesis: Interacting populations : random v.s. deterministic models
Supervisor : Laurent Serlet
Laboratory : : Laboratoire de Mathématiques Blaise Pascal
University : Clermont Auvergne University
Email and Phone : firstname.lastname@example.org, 04 73 40 70 93
Possible co-supervisor :
Modeling interacting populations is a subject that has already been widely studied. Such interaction can
be competition for food or, on the contrary, beneficial for both populations as for instance in the case of
male/female populations. Consequentely, according to the case considered and the model chosen, many different
behaviors can be observed. These models can be deterministic such as systems of differential equations (see
[Mu]) or random (Markov processes).
Figure 1 below is the representation of the joint evolution of males and females with initial unbalance.
The red discontinued line is the solution of the deterministic model whereas the blue trajectory is an instance of
the corresponding random model. In that case, the random trajectory is simply a noised version (more or less
according to the region) of the deterministic solution. But other phenomena can occur, as in Figure 2 where the
deterministic model predicts unbounded growth but the random model shows extinction.
The proposed work consists in selecting a few appropriate models and examining the relations between
random trajectories and deterministic solutions. Typically one expects that, under certain hypothesis,
convergence results hold when the numbers are big ; this is the « fluid » limit described in [DN] and the error term
is expected to be a diffusion. But one will also take interest in when and why the random model behaves
differently from the deterministic one.
Finally, it would be interesting to confront these models to real data, if such data can be found.
Prerequisites : differential equations ; Markov processes : chains, jump processes, diffusions, martingales (as
for instance in [Ku]) ; ability to perform simulations with Python.
First references :
[DN] Darling R.W.R., Norris J.R. Differential equation approximations for Markov chains.
Probab. Surveys (5) p. 37-79 (2008).
[Ku] Kurtz T.G. Lectures on stochastic analysis.
Download at : http://www.math.wisc.edu/~kurtz/735/main735.pdf
[Mu] Murray J.D. Mathematical Biology. Springer.
More informations via the link :
To apply, please download the application file via the link :
Interested students must send two copies of their application to the secretariat of the doctoral school before 22 May 2020, the deadline.
Audition at the doctoral school of the selected candidates:
- 4 June morning: LAMP jury
- 11th June morning: LMV jury
- 11 June afternoon: Chemistry jury
- 12 June: Physics jury
19 June: ED SF council for allocations Doctoral allocations
REQUIRED EDUCATION LEVELMathematics: Master Degree or equivalent
EURAXESS offer ID: 508385
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