A coupled model of fish-phytoplankton:
motion and evolution.
Yaya Youssouf
Department of Mathematics, Gaston-Berger University
Department of Mathematics, Uppsala University
First Network Meeting for Sida- and ISP-funded PhD Students in
Mathematics
Stockholm 7–8 March 2017
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My Advisors
Pr. Mamadou Sy
Pr. David J. T. Sumpter
Dr. Maksym Romenskyy
Main advisor
Gaston-Berger University
Assistant advisor
Uppsala University
Assistant advisor
Uppsala University
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Research Topic.
Interest
• Dynamic of populations.
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Research Topic.
Interest
• Dynamic of populations.
• Transport-diffusion models.
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Research Topic.
Interest
• Dynamic of populations.
• Transport-diffusion models.
Problematic
• How to construct a like Lotka-Voltera model to describe the dynamic
of fish-phytoplankton using a self-proppled particles (SPP) and agent
beased model (ABM)?
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Research Topic.
Interest
• Dynamic of populations.
• Transport-diffusion models.
Problematic
• How to construct a like Lotka-Voltera model to describe the dynamic
of fish-phytoplankton using a self-proppled particles (SPP) and agent
beased model (ABM)?
• Which transport-diffusion model should be associated to take in
account the motion of population ?
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Research Topic.
Interest
• Dynamic of populations.
• Transport-diffusion models.
Problematic
• How to construct a like Lotka-Voltera model to describe the dynamic
of fish-phytoplankton using a self-proppled particles (SPP) and agent
beased model (ABM)?
• Which transport-diffusion model should be associated to take in
account the motion of population ?
Goals
• Constuction of the model, full anlysis and simulations;
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Research Topic.
Interest
• Dynamic of populations.
• Transport-diffusion models.
Problematic
• How to construct a like Lotka-Voltera model to describe the dynamic
of fish-phytoplankton using a self-proppled particles (SPP) and agent
beased model (ABM)?
• Which transport-diffusion model should be associated to take in
account the motion of population ?
Goals
• Constuction of the model, full anlysis and simulations;
• Make a comparaison between Lotka-Voltera model.
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General view.
SPP
Self-propelled particles (SPP), is a concept used by physicists to describe
autonomous agents, which convert energy from the environment into
directed or persistent motiona .
Here are somme examples for autonomous agents:
Walking, swimming or flying animals;
a
Wikipedia
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General view.
SPP
Self-propelled particles (SPP), is a concept used by physicists to describe
autonomous agents, which convert energy from the environment into
directed or persistent motiona .
Here are somme examples for autonomous agents:
Walking, swimming or flying animals;
Bacteria, phytoplankton, cells, algae and other micro-organisms;
a
Wikipedia
4 / 10
General view.
SPP
Self-propelled particles (SPP), is a concept used by physicists to describe
autonomous agents, which convert energy from the environment into
directed or persistent motiona .
Here are somme examples for autonomous agents:
Walking, swimming or flying animals;
Bacteria, phytoplankton, cells, algae and other micro-organisms;
Any system of physical particles with coherent collective behavior for
exemple a robot system .
a
Wikipedia
4 / 10
General view.
SPP
Self-propelled particles (SPP), is a concept used by physicists to describe
autonomous agents, which convert energy from the environment into
directed or persistent motiona .
Here are somme examples for autonomous agents:
Walking, swimming or flying animals;
Bacteria, phytoplankton, cells, algae and other micro-organisms;
Any system of physical particles with coherent collective behavior for
exemple a robot system .
a
Wikipedia
The following pictures illustrates some autonomous agents.
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General view.
Figure: Spectacular folk of starlings.
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General view.
Figure: School of Fishs.
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General view.
Figure: traffic jam in Madagascar.
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General view.
Figure: A herd of zebra..
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A general SPP model
Figure: The two zona in the Vicsek-model.
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A general SPP model
Figure: The two zona in the Vicsek-model.
ri (t + τ ) = ri (t) + τ vi (t)
(1)
vi (t + τ ) = R(ξi (t))Vid (t)
(2)
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Impact and Applications of My Research
Impact
Find the basic laws describing the essential aspects of collective motion;
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Impact and Applications of My Research
Impact
Find the basic laws describing the essential aspects of collective motion;
Application
The applications are a lot and for many discipline:
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Impact and Applications of My Research
Impact
Find the basic laws describing the essential aspects of collective motion;
Application
The applications are a lot and for many discipline:
In mathematics, SPP and ABM gives an alternative for the usual
PDEs and ODEs models;
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Impact and Applications of My Research
Impact
Find the basic laws describing the essential aspects of collective motion;
Application
The applications are a lot and for many discipline:
In mathematics, SPP and ABM gives an alternative for the usual
PDEs and ODEs models;
In physic, SPP and ABM can be used to describe and understand
patterns of physicals systems as gases, crystals, liquids ...
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Impact and Applications of My Research
Impact
Find the basic laws describing the essential aspects of collective motion;
Application
The applications are a lot and for many discipline:
In mathematics, SPP and ABM gives an alternative for the usual
PDEs and ODEs models;
In physic, SPP and ABM can be used to describe and understand
patterns of physicals systems as gases, crystals, liquids ...
For society, one can solve the problems of crowd panic, trafic jam etc.
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Some patterns of fish, phytoplankton and coupled model
800
Fish
Number of particles
700
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Time
900
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Phase Map
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Fish
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Animation of fish-phytoplankton interaction
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Thank you!
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