Optimal pulse fishing policy in stage-structured models with birth pulses

Gao, Shujing; Chen, Lansun; Sun, Lixin

doi:10.1016/j.chaos.2004.11.093

Cited by 25 publications

(16 citation statements)

References 24 publications

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“…Although they have been initially developed for mechanical and electrical systems their applications to biological and environmental problems are growing. Tools of optimal control theory have been extensively used in renewable resource management (Clark 1990;Aniţa 1998;Jacobs et al 1991;Horwood and Whittle 1986;Kar 2004;Marutani 2008;White and Kendall 2007;Gao et al 2005;Mchich et al 2006). The present paper shows that the estimation problem in fisheries management can also be investigated from the point of view of control engineering.…”

Section: Resultsmentioning

confidence: 98%

On the stock estimation for some fishery systems

Guiro

Iggidr

Ngom

et al. 2009

Rev Fish Biol Fisheries

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In this work we address the stock estimation problem for two fishery models. We show that a tool from nonlinear control theory called ''observer'' can be helpful to deal with the resource stock estimation in the field of renewable resource management. It is often difficult or expensive to measure all the state variables characterising the evolution of a given population system, therefore the question arises whether from the observation of certain indicators of the considered system, the whole state of the population system can be recovered or at least estimated. The goal of this paper is to show how some techniques of control theory can be applied for the approximate estimation of the unmeasurable state variables using only the observed data together with the dynamical model describing the evolution of the system. More precisely we shall consider two fishery models and we shall show how to built for each model an auxiliary dynamical system (the observer) that uses the available data (the total of caught fish) and which produces a dynamical estimationxðtÞ of the unmeasurable stock state x(t). Moreover the convergence speed ofxðtÞ towards x(t) can be chosen.

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Section: Resultsmentioning

confidence: 98%

On the stock estimation for some fishery systems

Guiro

Iggidr

Ngom

et al. 2009

Rev Fish Biol Fisheries

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show abstract

“…q 1 = catchability coefficients of prey species, q 2 = catchability coefficients of predator species, E = common fishing efforts. Here r 1 , r 2 , α 11 , α 22 , α 12 and α 21 are all positive constants and known as biological parameters. The catch rate functions q 1 E x 1 and q 2 E x 2 are based on catch per unit effort (CPUE).…”

Section: Mathematical Formulation Of Fuzzy Prey-predator Modelmentioning

confidence: 99%

“…For the development of human society, it is undoubtedly essential problem how to utilize the biological resources. In the last decades, ordinary differential equations is used to present this type of problem and provide some mathematical answer and explanations [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. However, it is notable that the biological parameters used in the differential equations are not always fixed.…”

Section: Introductionmentioning

confidence: 99%

Stability and bionomic analysis of fuzzy parameter based prey–predator harvesting model using UFM

Pal

Mahapatra²,

Samanta

2014

Nonlinear Dyn

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In this paper, a novel concept of fuzzy preypredator model is introduced by considering the imprecise nature of the biological parameters. We consider the imprecise biological parameters as a form of triangular fuzzy number in nature. These imprecise parameters first transform to the corresponding intervals and then using interval mathematics the related differential equation is converted to two differential equations. Then using utility function method, the converted differential equations is changed to a single differential equation. The possibility of existence of both biological and bionomic equilibrium is presented. We obtain the conditions of local and global stability under impreciseness. We also study the optimal harvesting policy and derive the optimal solution under imprecise biological parameters. Lastly, numerical examples are presented to the support of our proposed approach.

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“…Impulsive equations [10,11] have been recently used in population dynamics in relation to impulsive vaccination [12], population ecology [13,14], the chemotherapeutic treatment of disease [15]. In addition, models with two impulses have been studied by Gao et al [16] and Liu et al [17].…”

Section: Introductionmentioning

confidence: 99%

A predator-prey system with two impulses on the diseased prey and a Beddington-DeAngelis response

Wang

Song

2009

Math. Meth. Appl. Sci.

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A predator-prey system with two impulses on the diseased prey is formulated and analyzed for the purpose of integrated pest management. The local and global stability of the susceptible pest-eradication periodic solution, as well as the permanence of the system, are obtained under the sufficient conditions by means of Floquet's theory for impulsive differential equations. Finally, we interpret our mathematical results.

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Optimal pulse fishing policy in stage-structured models with birth pulses

Cited by 25 publications

References 24 publications

On the stock estimation for some fishery systems

On the stock estimation for some fishery systems

Stability and bionomic analysis of fuzzy parameter based prey–predator harvesting model using UFM

A predator-prey system with two impulses on the diseased prey and a Beddington-DeAngelis response

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