Conservation of a prey-predator fishery with predator self limitation based on continuous fishing effort

Kar, Tapan Kumar; Pahari, U. K.; Chaudhuri, Kripasindhu

doi:10.1007/bf02935807

Cited by 9 publications

(5 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the following, we focus on the well known Rosenzweig-MacArthur prey-predator model (see e.g. [18], [19], [20], [21], [22], [23]) characterized by saturation of predation uptake, described by a Holling type II functional response, given by…”

Section: The Bioeconomic Modelmentioning

confidence: 99%

A prey–predator fishery model with endogenous switching of harvesting strategy

Bischi¹,

Lamantia²,

Radi³

2013

Applied Mathematics and Computation

View full text Add to dashboard Cite

We propose a dynamic model to describe a fishery where both preys and predators are harvested by a population of fishermen who are allowed to catch only one of the two species at a time. According to the strategy currently employed by each agent, i.e. the harvested variety, at each time period the population of fishermen is partitioned into two groups, and an evolutionary mechanism regulates how agents dynamically switch from one strategy to the other in order to improve their profits. Among the various dynamic models proposed, the most realistic is a hybrid system formed by two ordinary differential equations, describing the dynamics of the interacting species under fishing pressure, and an impulsive variable that evolves in a discrete time scale, in order to describe the changes of the fraction of fishermen that harvest a given stock. The aim of the paper is to analyze the economic consequences of this kind of self-regulating fishery, as well as its biological sustainability, in comparison with other regulatory policies. Our analytic and numerical results give evidence that in some cases this kind of myopic, evolutionary self-regulation might ensure a satisfactory trade-off between profit maximization and resource conservation.

show abstract

Section: The Bioeconomic Modelmentioning

confidence: 99%

A prey–predator fishery model with endogenous switching of harvesting strategy

Bischi¹,

Lamantia²,

Radi³

2013

Applied Mathematics and Computation

View full text Add to dashboard Cite

show abstract

“…We maximize the Hamiltonian in the equation 7 (13) We conclude that the total harvesting cost per unit effort equals to the discounted value of the future profit at the steady state [5,11]. By eliminating parameters 1  , 2  and 3  into equation 11, we obtain…”

Section: Optimal Harvesting Policymentioning

confidence: 99%

“…The fishery model of two competing species was addressed by Clark et al to discuss the aspect bionomics and the policy of optimal harvesting policy [2]. The combined harvesting of two competing species from the aspect of bionomic was also studied and discussed for the optimal equilibrium policy [3][4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Analysis of a Fishery Model with two competing prey species in the presence of a predator species for Optimal Harvesting

2018

View full text Add to dashboard Cite

A harvesting fishery model is proposed to analyze the effects of the presence of red devil fish population, as a predator in an ecosystem. In this paper, we consider an ecological model of three species by taking into account two competing species and presence of a predator (red devil), the third species, which incorporates the harvesting efforts of each fish species. The stability of the dynamical system is discussed and the existence of biological and bionomic equilibrium is examined. The optimal harvest policy is studied and the solution is derived in the equilibrium case applying Pontryagin’s maximal principle. The simulation results is presented to simulate the dynamical behavior of the model and show that the optimal equilibrium solution is globally asymptotically stable. The results show that the optimal harvesting effort is obtained regarding to bionomic and biological equilibrium.

show abstract

“…However, these studies have not included the harvesting effort as a variable in the modeling process. In actual, harvesting efforts are not constant but depend on the net revenue generated through the harvesting of a species [30][31][32][33][34]. Devi [35] has examined the impact of nonconstant harvesting of prey population in a ratio-dependent predator-prey system with prey refuge by taking harvesting effort as a dynamic variable in the modeling process.…”

Section: Introductionmentioning

confidence: 99%

A nonautonomous model for the effect of rarity value on the dynamics of a predator–prey system with variable harvesting

Singh,

Tiwari,

Verma

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

The human inclination to value rarity contributes to the exploitation of many wildlife species by driving up their market value when their numbers are scarce. This research investigates a model to explore how the value attached to rarity impacts the harvesting of predator species and subsequently influences the dynamics of predator–prey interactions in an ecological system. To broaden the model's scope, it's extended to its nonautonomous form by allowing the harvesting rate of predator species and the degree of neutrality in consumers to respond for the rarity of predator species to change over time. Both the autonomous and nonautonomous systems are explored through analytical and numerical investigation. Numerical findings reveal that as the prey population's growth rate gradually increases, the unforced system shifts from stable boundary equilibrium (harvesting absent) to stable interior equilibrium, then to oscillatory interior equilibrium, followed by period doubling oscillations leading to chaotic behavior. The autonomous system exhibits limit cycle oscillations around the boundary equilibrium when predator species are minimally harvested. Moderate harvesting stabilizes the system, while excessive harvesting induces instability. However, the chaotic oscillations can be eliminated through period‐halving route upon decreasing the consumers' response to predator rarity. Furthermore, the seasonally forced model demonstrates periodic solutions, higher order periodic solutions, and chaotic dynamics contingent upon different settings of prey growth rate, the strength of seasonality in predator harvesting, and the consumers' response to predator rarity.

show abstract

Conservation of a prey-predator fishery with predator self limitation based on continuous fishing effort

Cited by 9 publications

References 12 publications

A prey–predator fishery model with endogenous switching of harvesting strategy

A prey–predator fishery model with endogenous switching of harvesting strategy

Analysis of a Fishery Model with two competing prey species in the presence of a predator species for Optimal Harvesting

A nonautonomous model for the effect of rarity value on the dynamics of a predator–prey system with variable harvesting

Contact Info

Product

Resources

About