A model for fishery resource with reserve area

Dubey, B.; Chandra, Peeyush; Sinha, Prawal

doi:10.1016/s1468-1218(02)00082-2

Cited by 98 publications

(81 citation statements)

References 23 publications

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“…Dynamic models for commercial fishing have been widely studied in the light of economic and ecological factors [6,7]. In recent decades there has been considerable interest for modeling the dynamics of fisheries resources systems [2,4,5,10,15]. Chaudhuri [3] proposed a model for two species of fish competitors, each of which develops logistically.…”

Section: Introductionmentioning

confidence: 99%

“…They discussed the biological and bionomic balance and the optimal harvesting policy. Dubey et al [10] also proposed and analyzed a shore-to-sea fishing model where the fish population is harvested in both zones. Then they studied the stability analysis and optimal harvest policy taking taxation as a control instrument.…”

Section: Introductionmentioning

confidence: 99%

“…Then they studied the stability analysis and optimal harvest policy taking taxation as a control instrument. Louartassi et al [16] has studied the coastal sea-fishing model where the fish population is harvested in two areas of Dubey et al [10] where he propose a comprehensive state regulation by output feedback based on a Lyapunov function. Sharma et al [19] proposed a study the dynamics of fishery resource with reserve area in the presence of bird predator.…”

Section: Introductionmentioning

confidence: 99%

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Harvesting model for fishery resource with reserve area of bird predator and modified effort function

Louartassi¹,

Alami²,

Elalami³

2017

Malaya J. Mat.

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The purpose of this paper is to study the dynamics of fisheries resources with reserve area, in the presence of bird predators. Aquatic area under investigation is divided into two areas : one for the free fishing and other limited for any type of fishing. In the project harvesting system according to the modified E effort is considered, which depends on the effect of resource density. The local and stability criteria, the overall stability and instability are established for the project model. Finally, the theoretical results are illustrated by numerical simulations in the last section.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Harvesting model for fishery resource with reserve area of bird predator and modified effort function

Louartassi¹,

Alami²,

Elalami³

2017

Malaya J. Mat.

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“…Since the pioneer work of Lotka-Volterra model many complex models are developed to study prey-predator interactions involving different types of factors [1]. The existence of reserved zone to protect the prey has become an important factor of prey-predator systems and its effects on stability have been focused in several models [2][3][4][5]. Most of these studies have been observed that use of refuges by prey has a stabilizing effect on prey-predator dynamics.…”

Section: Introductionmentioning

confidence: 99%

A prey - partially dependent predator with a reserved zone: modelling and analysis

Murthy

Khaled

2015

IJAMR

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<p>In this paper, a mathematical model consisting of a prey-partially dependent predator has been proposed and analyzed. It is assumed that the prey moving between two types of zones, one is assumed to be a free hunting zone that is known as an unreserved zone and the other is a reserved zone where hunting is prohibited. The predator consumes the prey according to the Beddington-DeAngelis type of functional response. The existence, uniqueness and boundedness of the solution of the system are discussed. The dynamical behavior of the system has been investigated locally as well as globally with the help of Lyapunov function. The persistence conditions of the system are established. Local bifurcation near the equilibrium points has been investigated. Finally, numerical simulation has been used to specify the control parameters and confirm the obtained results.</p>

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“…They have also discussed the conservation of the prey population and analyzed the behavioral dependency of the predator population on the reserve capacity. Dubey et al [27] analyzed a mathematical model to study the dynamics of a fishery resource system in an aquatic environment that consists of two zones, one was free fishing area and another was reserve area. It may also be noted that prey-predator interactions do matter when the implementation of a reserve is considered in the system and reserves will be most effective when coupled with fishing effort controls in adjacent fisheries [28][29][30].…”

Section: Introductionmentioning

confidence: 99%

An ecological perspective on marine reserves in prey–predator dynamics

Chakraborty

Das²,

Kar

2013

J Biol Phys

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This paper describes a prey-predator type fishery model with prey dispersal in a two-patch environment, one of which is a free fishing zone and other is a protected zone. The existence of possible steady states, along with their local stability, is discussed. A geometric approach is used to derive the sufficient conditions for global stability of the system at the positive equilibrium. Relative size of the reserve is considered as control in order to study optimal sustainable yield policy. Subsequently, the optimal system is derived and then solved numerically using an iterative method with Runge-Kutta fourth-order scheme. Numerical simulations are carried out to illustrate the importance of marine reserve in fisheries management. It is noted that the marine protected area enables us to protect and restore multi-species ecosystem. The results illustrate that dynamics of the system is extremely interesting if simultaneous effects of a regulatory mechanism like marine reserve is coupled with harvesting effort. It is observed that the migration of the resource, from protected area to unprotected area and vice versa, is playing an important role towards the standing stock assessment in both the areas which ultimately control the harvesting efficiency and enhance the fishing stock up to some extent.

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A model for fishery resource with reserve area

Cited by 98 publications

References 23 publications

Harvesting model for fishery resource with reserve area of bird predator and modified effort function

Harvesting model for fishery resource with reserve area of bird predator and modified effort function

A prey - partially dependent predator with a reserved zone: modelling and analysis

An ecological perspective on marine reserves in prey–predator dynamics

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