Ecological dynamics of age selective harvesting of fish population: Maximum sustainable yield and its control strategy

Jana, Dipak Kumar; Agrawal, Rashmi; Upadhyay, Ranjit Kumar; Samanta, G. P.

doi:10.1016/j.chaos.2016.09.021

Cited by 14 publications

(5 citation statements)

References 37 publications

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“…13 (e),(f),(g)) 2 ϑ 1 < 2. 24 Population is positively invariant, permanent, globally stable and ϑ 2 = 1 periodic. (Fig.…”

Section: Discussionmentioning

confidence: 99%

“…14 (a)) ϑ 1 = 2. 24 Population curve(s) become unbounded i.e, It is not positively invariant ϑ 2 = 1 nor permanent nor globally stable nor periodic. 2.24 ϑ 1 3…”

Section: Discussionmentioning

confidence: 99%

“…It is also assumed that the death rate and intraspecific competition rate both together contribute to the rate of decline, which is instantaneous. The death rate is represented using a linear term and a quadratic term is used to describe the rate of intraspecific competition [24]. Now in our model we will assume that individuals of hilsa fish which are born before a time ϑ 1 from the present instant t are sexually able to give rise to new offspring and we can harvest for our economic profit those hilsa fishes which are born before ϑ 2 time from now (t).…”

Section: Introductionmentioning

confidence: 99%

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Interplay between reproduction and age selective harvesting delays of a single population non-autonomous system

Devi

Jana

Lakshmanan

2020

Preprint

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This paper is concerned with an analysis of the dynamics of a non-autonomous, single population age based growth model with harvesting formulation. First, we derive sufficient conditions for permanence and positive invariance. Then, by constructing a scalar function, namely the Lyapunov function, we arrive at a suitable criterion for global attractivity. With the help of Brouwer fixed point and continuation theorems, we obtain constraints for the existence of a positive periodic solution. Then we prove that there exists only one solution which is almost periodic in nature that is distinct from every other solution. Further, we carry out a numerical simulation to support the analytical findings.

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“…13 (e),(f),(g)) 2 ϑ 1 < 2. 24 Population is positively invariant, permanent, globally stable and ϑ 2 = 1 periodic. (Fig.…”

Section: Discussionmentioning

confidence: 99%

“…14 (a)) ϑ 1 = 2. 24 Population curve(s) become unbounded i.e, It is not positively invariant ϑ 2 = 1 nor permanent nor globally stable nor periodic. 2.24 ϑ 1 3…”

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interplay between reproduction and age selective harvesting delays of a single population non-autonomous system

Devi

Jana

Lakshmanan

2020

Preprint

Self Cite

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“…The fact that species do not naturally exist in isolation but coexist, compete or serve as prey for others, led to extensive literature on harvesting of a single or multiple populations in a food chain, and on optimal yields for exploited species [24,25,26,27]. Incorporating harvesting in systems of differential or difference equations includes the case of structured populations where selective harvesting is allowed [28,29]. This approach is quite useful in policy-making, for example, when only fish types within a certain size range are eligible to take-home vs catch-and-release policies.…”

Section: Introductionmentioning

confidence: 99%

Optimality and sustainability of delayed impulsive harvesting

Lawson,

Braverman

2022

Preprint

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We consider a logistic differential equation subject to impulsive delayed harvesting, where the deduction information is a function of the population size at the time of one of the previous impulses. A close connection to the dynamics of high-order difference equations is used to conclude that while the inclusion of a delay in the impulsive condition does not impact the optimality of the yield, sustainability may be highly affected and is generally delay-dependent. Maximal and other types of yields are explored, and sharp stability tests are obtained for the model, as well as explicit sufficient conditions. It is also shown that persistence of the solution is not guaranteed for all positive initial conditions, and extinction in finite time is possible, as is illustrated in the simulations.

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“…First, it is prototypical for many biological, chemical, and medical processes as it captures the most basic dynamic behavior of oscillatory systems. Second, for fishing systems our basic assumption of a slow process with expensive measurements applies and processes related to sustainable fishing have been receiving increasing attention lately, e.g., [44,45]. Third, it has a prototypical objective for many medical applications, as we want to control from an undesired cyclic steady state to a desired steady state.…”

Section: Introductionmentioning

confidence: 99%

A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

Jost

Säger

2017

Processes

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Nonlinear model predictive control has been established as a powerful methodology to provide feedback for dynamic processes over the last decades. In practice it is usually combined with parameter and state estimation techniques, which allows to cope with uncertainty on many levels. To reduce the uncertainty it has also been suggested to include optimal experimental design into the sequential process of estimation and control calculation. Most of the focus so far was on dual control approaches, i.e., on using the controls to simultaneously excite the system dynamics (learning) as well as minimizing a given objective (performing). We propose a new algorithm, which sequentially solves robust optimal control, optimal experimental design, state and parameter estimation problems. Thus, we decouple the control and the experimental design problems. This has the advantages that we can analyze the impact of measurement timing (sampling) independently, and is practically relevant for applications with either an ethical limitation on system excitation (e.g., chemotherapy treatment) or the need for fast feedback. The algorithm shows promising results with a 36% reduction of parameter uncertainties for the Lotka-Volterra fishing benchmark example.

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Ecological dynamics of age selective harvesting of fish population: Maximum sustainable yield and its control strategy

Cited by 14 publications

References 37 publications

Interplay between reproduction and age selective harvesting delays of a single population non-autonomous system

Interplay between reproduction and age selective harvesting delays of a single population non-autonomous system

Optimality and sustainability of delayed impulsive harvesting

A Feedback Optimal Control Algorithm with Optimal Measurement Time Points

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