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Optimal spatial distribution of a bioeconomicalfishing model on 3 zonesR. Mchich 1 , P. Auger 2 , H. Hbid 3 and N. Raïssi 41 E.N.C.G., B.P. 1255, Tanger Principale, Maroc.2 UR GEODES, IRD, Centre de Recherche d’Ile de France,32 av. Henri Varagnat,93143 Bondy cedex, France.3 Laboratoire LPSSD, Faculté des Sciences Semlalia, B.P. 2390, Marrakech, Maroc.4 Laboratoire SIANO, Faculté des Sciences, Université Ibn Tofaïl, B.P.133, Kénitra, Maroc.ABSTRACT. This work presents a stock-effort bio-economical model of a fishery subdivided on threefishing zones. The stock corresponds to a fish population moving between different zones, on whichthey are harvested by fishing fleets. We take profit from the existence of two time scales (a fastone for fish migration and fleets movements, and a slow one for fish growth and mortality and fleetsrevenue) to construct a reduced (aggregated) model. The mathematical analysis of the model allowsthe optimization of the spatial distribution of the fishing effort, and so on the control of the fleetsdisplacement between the fishing zones, in order to increase the total activity.RÉSUMÉ. Ce travail présente un modèle bioéconomique de pêche, stock-effort distribué sur troiszones. Le stock correspond à une population de poissons se déplaçant entre les différentes zones,sur lesquelles elle est exploitée par des flottes de pêche. Nous tirons profit de l’existence de deuxéchelles de temps (une rapide pour les migrations et une lente pour la croissance et la mortalitédes poissons et pour les revenus des flottes) pour construire un modèle réduit (agrégé). L’étudemathématique de ce modèle permet l’optimisation de la distribution spatiale des efforts de pêche,et par suite le contrôle du déplacement des flottes entre les différentes zones de pêche dans le butd’accroître l’activité de pêche globale.KEYWORDS : Fishery model, aggregation of variables, optimal spatial distribution of fishing effort.MOTS-CLÉS : Modèle de pêche, agrégation des variables, distribution spatiale optimale des effortsde pêche.TAMTAM –Tunis– 2005 540
Bioeconomical fishing model 5411. IntroductionThe overexploitation of marine resources and the continuous high pressure on fishstocks leads inexorably to their extinction and to a global and worrying decrease in thelevel of catch. For example, in [6], authors study the evolution of Brittany’s industrialfleets and show an important decrease of their overall fishing power in the eighties forsaithe, cod, haddock and whiting in the West of Scotland area. An other important case isalso that of the pelagic resources, which represent 75 percent of the Atlantic fish stock inNorth-West Africa (see [8]). In Morocco, drastic fluctuations of abundance have been observedfor sardines and other pelagic during the last fifty years. This situation interpellatesthe responsible of fishery management, for making appropriate decisions, as controllingthe repartition of the fleets on different fishing zones, in order to avoid a potential slumpin the sector, and the aim of this work is to study the optimal spatial distribution of thefishing effort in a multi fishing zone, and to give some efficient management measures, bycontrolling the displacement of the fleets between the fishing zones, in order to increasethe total activity.In section 2, we present the complete fishing activity model on three zones. It consistsin a system of six ordinary differential equations governing the three local fishing stocksand the three fishing efforts on three adjacent fishing zones. We assume two time scales: afast one associated to the quick movements between different zones, and a slow one whichcorresponds to the growth of fish populations and the variation of the fleets revenue. Thegrowth of the fish is related to the natural demography rate (with Allee effect) less themortality rate due to the fishery, whereas the fishery fleet’s growth is function of the profitgenerated by the activity, which could be interpreted as an investment. We recall that wetake advantage of the two time scales to reduce the complete models by use of aggregationmethods (one can see the review article on aggregation techniques by Auger and Bravo dela Parra [1]). The analysis of the corresponding aggregated model leads to a level of totalsustainable fishing activity function of the spatial distribution of the fishing effort. That isthe spatial distribution could be chosen in order to maximize this total equilibrium level.Section 3 is devoted to a discussion/conclusion.2. The 3 fishing zones modelThe complete model: We consider a fish population harvested by a fishing fleet.Fishing boats are allowed to exploit the resource on three fishing zones. Let N(t) bethe fish population density at time t: N(t) = (n 1 (t), n 2 (t), n 3 (t)) T . n 1 (t) (resp. n 2 (t)and n 3 (t)) is the fish population density on fishing area 1, (resp. 2 and 3), at time t.Similarly, the fishing effort is subdivided into three components on each fishing zone:E(t) = (E 1 (t), E 2 (t), E 3 (t)) T . E i (t) is the fishing effort on fishing area i (i = 1, 2, 3),TAMTAM –Tunis– 2005
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PréfaceOrganiser la seconde éditi
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Comité d’organisationMohamed Abd
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SOMMAIRE / CONTENTSI Conférences I
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Equilibre dans un système dynamiqu
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Arlequin method: Practical impacts
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Application de la méthode de Gauss
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Conférences InvitéesInvited Prese
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4 Amara et al.1. IntroductionWe are
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6 Amara et al.2.2. The nonlinear Na
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8 Amara et al.4. Numerical resultsW
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10 Auger et al.1. Introduction :Dan
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12 Auger et al.La condition de stab
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14 Auger et al.3.1. Taux de migrati
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16 Auger et al.L’équilibre rapid
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18 Auger et al.[7] BRAVO DE LA PARR
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Quelques aspects mathématiques etn
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22 El Alaoui Talibi M.- Modèle d
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24 El Alaoui Talibi M.[3] M. Chamba
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26 Habbal1. IntroductionAngiogenesi
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28 HabbalThe pressure drop denoted
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30 Habbaltheorem 1 There exists a N
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32 HabbalFigure 2. Second Nash loop
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34 Hauray et al.1. IntroductionWe a
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36 Hauray et al.minimal time interv
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38 Hauray et al.From this last theo
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Approximation de l’opérateur d
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42 LemrabetLorsque δ → 0, l’é
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44 Lemrabetavec[∆ ∗ (δ)c = [I
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46 Lemrabet6. Bibliographie[1] N. B
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48 Jaafar-Belaid et al.1. Introduct
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50 Jaafar-Belaid et al.where f(ρ)
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52 Jaafar-Belaid et al.202040406060
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IIContrôleControl55
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58 Arfaoui1. IntroductionCe travail
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60 ArfaouiLe système adjoint assoc
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62 Arfaoui[3] H. ARFAOUI , « Comma
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64 Benzekri et al.1. Global control
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66 Benzekri et al.ẏ = ∂H∂x =
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0 1 2 3 4 5 668 Benzekri et al.32.5
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70 Akian et al.1. IntroductionWe co
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72 Akian et al.We prove that v t+δ
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.74 Akian et al.0.0−1.0Exact solu
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76 Bokanowski et al.1. General fram
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78 Bokanowski et al.One interesting
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80 Bokanowski et al.4. Numerical ex
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Sur les problèmes de contrôle opt
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84 Metouileur lorsque u est dans L
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86 MetouiThéorème 2 Soit ū ε le
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88 Metoui[5] L.S. HOU, S.S. RAVINDR
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Système d’information intégré
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Gestion et modélisation des ressou
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Random perturbations of reduced gra
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Global Optimization of Water Resour
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Global Optimization of Water Resour
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IVEquations DifférentiellesDiffere
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114 B. Abdelkader1. IntroductionTel
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116 B. AbdelkaderNotons que les con
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118 B. AbdelkaderAlors pour tout X
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120 Bouzahir1. IntroductionWe consi
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122 Bouzahirwhere the linear operat
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Goursat boundary value problem forh
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126 A. Guezane-Lakoud et al.3. Func
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128 A. Guezane-Lakoud et al.5. Exis
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ACP neuronale : application à l’
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132 Chitroubl’approximation de la
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134 Chitroubcompression égal à 3.
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136 Chitroub[4] J. P. Nougier, Mét
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138 Ferchichi et al.1. Introduction
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140 Ferchichi et al.soit T −1 = (
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142 Ferchichi et al.[4] G.I. BISCHI
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144 Hafidi1. IntroductionOn étudie
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146 Hafidia ) ∫ Ωpdx → +∞ qu
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148 HafidiLEMME 3.2. On a lim R(θ
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150 Lefebvre1. IntroductionSoit (X
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152 LefebvreOn peut aussi écrire q
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154 Lefebvre5. BibliographieD.R. Co
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156 Meskine1. IntroductionDans le p
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158 Meskinefaibles σ( ∏ L M ,
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160 Meskine[12] E. YA. KHRUSLOV, L.
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162 K. Saoudi1. IntroductionL’ét
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164 K. Saoudice qui montre que la s
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166 K. Saoudieton aboutit au résul
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168 K. Saoudietc 1 + c 2 = 1 ∫(u
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170 K. SaoudiRemarque 3.1. Du lemme
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172 K. Saoudiet∫v(t, x) dxΩest c
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VEstimation d’ErreursError Estima
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178 Achchab et al.1. IntroductionDu
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180 Achchab et al.such that}Xh 2 ={
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182 Achchab et al.[2] B.ACHCHAB, M.
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184 Alla et al.1. IntroductionLes e
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186 Alla et al.3. Position du probl
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IsoValue-0.00070533-0.000604452-0.0
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190 Achchab et al.1. IntroductionLe
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192 Achchab et al.où T hi/2 est le
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IsoValue0.000933570.002800710.00840
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196 El Dabaghi et al.1. Motivation
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198 El Dabaghi et al.0 ≤ λ i ≤
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200 El Dabaghi et al.Figure 4. Mail
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Residual error estimators for the t
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204 Kharrat et al.The step (3) need
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206 Kharrat et al.following estimat
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VIMécanique des FluidesFluid Mecha
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212 Abdelwahed et al.1. Introductio
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214 Abdelwahed et al.Ainsi, suivre
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216 Abdelwahed et al.Figure 3. Isov
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Procédure spectrale avec diagonali
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220 El Guarmah et al.où Ra et P r
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222 El Guarmah et al.M 10 20 25 35
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Simulation de l’onde de crue via
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226 El Dabaghi et al.de R 2 , de fr
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228 El Dabaghi et al.INRIA-MODULEFm
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INRIA-MODULEF230 El Dabaghi et al.I
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232 Amoura et al.1. IntroductionFor
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234 Amoura et al.where u = rot r ψ
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236 Amoura et al.CURRENT FUNCTION5
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238 Frih et al.1. IntroductionLa mo
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240 Frih et al.et dans la fracture,
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242 Frih et al.6. Bibliographie[1]
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244 Hasnaoui et al.1. IntroductionL
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246 Hasnaoui et al.On obtient alors
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248 Hasnaoui et al.5. Conclusion et
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250 Hernane-Boukari1. IntroductionW
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252 Hernane-Boukarianda 3 =−11 +
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254 Kloucha et al.1. Motivation et
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256 Kloucha et al.Si le domaine Λ
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INRIA-MODULEF0INRIA-MODULEF.250INRI
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Dimensions fractales : attracteurs
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262 Lamrini Uahabi et al.4. Attract
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264 Lamrini Uahabi et al.l 0 = λ
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266 Lamrini Uahabi et al.En conséq
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Numerical analysis for the problem
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270 El-Kyal et al.d(u) = 1 2(∇u +
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272 El-Kyal et al.Theorem 3.1 There
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274 Marchand et al.1. IntroductionD
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276 Marchand et al.On remarque en p
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278 Marchand et al.dans la formulat
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280 Mezali et al.1. Motivation et m
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282 Mezali et al.s’annulant sur c
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284 Mezali et al.Temps CPUTemps Ela
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R. Touihri & S. Ghnimi *Méthode de
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288 Touihri et al.Les équations go
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290 Touihri et al.Tol N It (Newt) t
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292 Touihri et al.5. Bibliographie[
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Décomposition de domaine pour un m
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DDM pour les fractures 297et−→
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DDM pour les fractures 299dont l’
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Arlequin method: Practical impacts
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Arlequin method 303of the Arlequin
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Arlequin method 3052.2. Penalized A
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Arlequin method 307refinements of t
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Reduction methods and uncertaintypr
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Reduction methods and uncertainty p
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Reduction methods and uncertainty p
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0.00e+00 1.00e−11 2.00e−11 3.00
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Homogénéisation d’un problème
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Problème de conduction-rayonnement
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Problème de conduction-rayonnement
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Equation d’Hamilton-Jacobi 3231.
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Equation d’Hamilton-Jacobi 325qui
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0Equation d’Hamilton-Jacobi 3272
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Détermination du nombre de région
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Simulation des courants de Foucault
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Une méthode d’accélération de
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Schéma SRNHS 3491. IntroductionUn
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Schéma SRNHS 3513. Application du
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Schéma SRNHS 3535. ConclusionLes r
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Smoothing and compressing surfaces
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Problème de convection en milieu p
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0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0
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Condensation de masse pour la méth
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Condensation de masse 367montre que
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Condensation de masse 369Le terme h
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Condensation de masse 371Aet Qile f
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VIIIModèles CinétiquesKinetic Mod
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376 Ben Abdallah et al.1. Introduct
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378 Ben Abdallah et al.where B ∓
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380 Ben Abdallah et al.ture that th
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382 Degond et al.1. IntroductionOn
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384 Degond et al.q φ s (x, t)/(|q|
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386 Degond et al.Enfin l’opérate
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Les métaheuristiques : application
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Les métaheuristiques 391simulé fu
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Les métaheuristiques 393Fig. 1 Dia
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Les métaheuristiques 395Fig.4 : R
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Prices after capacity addition in m
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Multi-user elastic demand communica
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Shape optimization 4051. Introducti
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Shape optimization 4072.1. Variatio
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Shape optimization 409(a)(b)(c)(d)F
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Problèmes d’optimisation en éco
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Assimilation de données pour l’e
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Écart à la Réciprocité et ident
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Identification de fissures planes 4
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Algorithme de Kohn et Vogelius 4331
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Algorithme de Kohn et Vogelius 435l
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Algorithme de Kohn et Vogelius 4375
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Résolution d’un problème de Cau
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Problème inverse géométrique 445
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Identification de fissures 4511. In
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−0.5 −0.4 −0.3 −0.2 −0.1
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Application de l’algorithme deNeu
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Complétion de données en élastic
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Complétion de données en élastic
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Analytic extensions on an annulus:a
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Analytic extensions on an annulus 4
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Analytic extensions on an annulus 4
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−1 −0.8 −0.6 −0.4 −0.2 0
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Cauchy problem for Laplace’s equa
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Modélisation asymptotique des onde
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Ondes de relief 479 uuuv 1 1 pu v
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Ondes de relief 481( )ˆeiZw( C e D
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Ondes de relief 4836. Bibliographie
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Régularisation pour l’aéroacous
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Régularisation pour l’aéroacous
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Page 534 and 535: 516 Achchab1. IntroductionDans la m
Page 536 and 537: 518 AchchabNous montrons dans le pa
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Page 540 and 541: 522 Derbel et al.1. IntroductionLa
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Page 548 and 549: 530 El Saadiwhere δ Xi(t) is the D
Page 550 and 551: 532 El Saadi5. References[1] A. L.
Page 552 and 553: 534 Ben Miled et al.1. Introduction
Page 554 and 555: 536 Ben Miled et al.nature de l’e
Page 556 and 557: 538 Ben Miled et al.Ensuite on étu
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Page 562 and 563: 544 Mchich et al.3∑where r = r i
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Page 568 and 569: 550 Ayadi1. IntroductionConsider a
Page 570 and 571: 552 AyadiFor all 0 ≤ p ≤ i, P p
Page 572 and 573: 554 AyadiFigure 3. The curves above
Page 574 and 575: Analyse mathématique et numérique
Page 576 and 577: 558 Chamekh et al.2. Modèle de tig
Page 578 and 579: 560 Chamekh et al.Γ sr(s)r(σ)Figu
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Page 582 and 583: 564 RahmaniI 2 étant l’identité
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Page 588 and 589: 570 Saidoù u vérifie :n∑n∑j=1
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590 Hlaoui1. IntroductionMore and m
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592 Hlaoui3. The New Graph Represen
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594 Hlaoui1 1 2 3 4 1 1 3 411 421 4
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596 M. Nekri et al.1. IntroductionL
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598 M. Nekri et al.proposés. Ces m
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600 M. Nekri et al.cycle de longueu
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