[Mini-course] Dynamical System and Its Applications in Ecology


Invited speakers:

1. Professor Pierre AUGER

Member of French Academy of Science, France.

Institute of Research for Development (IRD), France.

2. Researcher Tri NGUYEN-HUU

ENS Lyon, France.

Institute of Research for Development (IRD), France.



Morning session

Time:  9h00-11h30: Pierre AUGER

Place: VIASM Lecture Hall B4, the 7th floor, Ta Quang Buu Library, University of Science and Technology

Title: Reduction of Complexity of Dynamical Systems: Applications to Fishery Modelling

Abstract: Population and community models are complex in the sense that they usually take into account many variables and parameters. We present methods allowing the reduction of the dimension of the system which may become, in this way, mathematically more tractable. The reduction of the proposed system is undertaken with the help of aggregation methods which aim at studying the relationships between a large class of complex systems, in which many variables are involved, and their corresponding reduced or aggregated systems, governed by a few variables. The kind of aggregation methods that we consider is based on time scale separation methods. In order to illustrate the methods in population and community dynamics, we present an application of aggregation methods in multi-site fishery modelling. The different sites can correspond to fishing areas, Marine Protected Areas (MPA), or still Fish Aggregating Devices (FAD).
We present modelling examples :
• We consider a multi-site stock-fishing effort model. We show that the total catch can be optimized for a given number of FADs.
• We study the effects of fast price variation as a result of demand and supply on the global dynamics of a fishery. We study cases of linear as well as non-linear demand functions of price.
• We present a model of a commercial species, the “thiof” in Senegal, showing drastic decreasing catch with a booming market price.
• We study the effects of Artificial Habitats on the dynamics of a fishery with a fishing area and a MPA.


Afternoon session

Time: 14h30-16h30: Tri NGUYEN-HUU

Place: Room 106B-D3, School of Applied Mathematics and Informatics, Hanoi University of Science and Technology.

Title: Reduction of complexity of dynamical systems and ecological applications

Abstract. We present methods of reduction of complexity in dynamical systems, called aggregation of variables, and their use in ecological modelling. In particular, we focus on
the case of discrete systems and Leslie models. Such methods allow to lower the the dimension of the system (number of equations) taking profit from time scale differences, in order to make it easier to analyse. We study the way to build an aggregated model in several cases and remind the way to perform the analysis. Such methods will be illustrated by ecological applications: modelling of large herbivors in Kenya National Parks (for continuous models) 
and modelling of the dynamics of a beetle in west France (for discrete models).

1. AUGER P., BRAVO DE LA PARRA R., POGGIALE J.C., SANCHEZ E., NGUYEN HUU T., Aggregation of variables and applications to population dynamics. In: P. Magal, S. Ruan (Eds.), Structured Population Models in Biology and Epidemiology, Lecture Notes in Mathematics, vol. 1936, Mathematical Biosciences Subseries. Springer, Berlin, 2008, p. 209-263.
2. AUGER P., R. BRAVO DE LA PARRA, J.C. POGGIALE, E. SANCHEZ, L. SANZ, Aggregation methods in dynamical systems variables and applications in population and community dynamics, Physics of Life Reviews, 5, pp. 79-105, 2008.
3. AUGER P. and DUCROT A. A model of fishery with fish stock involving delay equations. PTRSA : Philosophocal Transactions of the Royal Society A. 367, pp. 4907-4922, 2009.
4. AUGER P., MCHICH R., RAÏSSI N., KOOI B. Effects of market price on the dynamics of a spatial fishery model: Over-exploited fishery/traditional fishery. Ecological Complexity, 7, pp. 13-20, 2010.
5. AUGER P., LETT C., MOUSSAOUI A. and PIOCH S.. Optimal number of sites in artificial pelagic multi-site fisheries. Canadian Journal of Fisheries and Aquatic Sciences. 67, pp. 296-303, 2010.
6. LY S., AUGER P. & BALDE M. A bioeconomic model of a multi-site fishery with non linear demand function: Number of sites optimizing the total capture. Acta Biotheoretica, 2014, 62 (3), p. 371-384.
7. MANSAL F., AUGER P. & BALDE M. A mathematical model of a fishery with variable market price. Sustainable fishery/over- exploitation. Acta Biotheoretica, 2014, 62 (3), p. 305-323.
8. MOUSSAOUI A., BENSENANE M., AUGER P. & BAH A. On the optimal size and number of reserves in a multi-site fishery model. Journal of Biological Systems, 2015, 23 (1), p. 1-17.
9. BROCHIER T., AUGER P., THIAM N., SOW M., DIOUF S. & BREHMER P. Implementation of artificial habitats, inside or outside the marine protected areas? Insights from a mathematical approach, Ecol. Modelling. 2015. Accepted.

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