Ecological chaos and the choice of optimal harvesting policy

Upadhyay, Ranjit Kumar; Tiwari, Satish Kumar

doi:10.1016/j.jmaa.2016.11.054

Cited by 22 publications

(13 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this work, we have provided evidence for the small changes of fractional orders that can provide a significant impact on the dynamic behavior of the LV system. In the literature, several valuable results such as stability analysis, persistence, permanence, and extinction are studied about the LV system (see [18][19][20][21][22][23][24][25][26][27][28][29]).…”

Section: Introductionmentioning

confidence: 99%

“…One of the best strategies is to apply the harvesting force as a control parameter on the particular individuals that are contributing to the damage (see [25]). In the literature (see [26][27][28][29]), many authors studied the LV system with the harvesting effect. From this analysis, we can observe that the immigration and harvesting effects having much influence on the stability of the LV system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Kaviya

Muthukumar

2021

Eur. Phys. J. Plus

View full text Add to dashboard Cite

Aim of this work is to study the four species various fractional-order prey-predator or Lotka-Volterra (LV) system with both immigration and harvesting effects. The existence and uniqueness, uniform boundedness, persistence, permanence, and extinction of this system solution are analyzed. The stability behavior of the system is obtained with the help of the Routh-Hurwitz (RH) stability criterion. The small changes in fractional-order values can produce a significant impact on the stability of the system is confirmed. This work verifies that the small amount of immigration effect can change the dynamic nature of the LV system. Numerical results are given to illustrate the obtained theoretical results of the stability analysis. The bionomic equilibrium points of the system are attained with their feasibility conditions. To get the optimal amount of harvesting effect with the Pontryagin's maximum principle, the harvesting parameter is considered as the control parameter.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Kaviya

Muthukumar

2021

Eur. Phys. J. Plus

View full text Add to dashboard Cite

show abstract

“…Additionally, the nonselective harvesting of both populations is taken into consideration. Recently, many research results related to how harvesting efforts affect plankton-fish dynamics or predatorprey dynamics have been reported [21][22][23][24][25][26]. Panja et al [22] indicate that the harvesting effort plays an important role in the stability of the phytoplankton-zooplankton-fish system.…”

Section: Introductionmentioning

confidence: 99%

“…Panja et al [22] indicate that the harvesting effort plays an important role in the stability of the phytoplankton-zooplankton-fish system. Upadhyay et al [23] summarized that a variation of harvesting term can generate rich dynamics such as limit cycles and chaos in plankton system. Then the following dynamical system proposed as a simple model of phytoplankton-fish interaction:…”

Section: Introductionmentioning

confidence: 99%

Dynamical analysis of a stochastic toxin-producing phytoplankton–fish system with harvesting

Liao

Dai

et al. 2020

Adv Differ Equ

View full text Add to dashboard Cite

In this paper, we analytically and numerically study the dynamics of a stochastic toxin-producing phytoplankton–fish system with harvesting. Mathematically, we give the existence and stability of the positive equilibrium in the deterministic system (i.e., the system without environmental noise fluctuations). In the case of the stochastic system (i.e., the system with environmental noise fluctuations), in addition to the existence and uniqueness of the positive solution, we provide the properties of the stochastic dynamics including the stochastic extinction and persistence in the mean, almost sure permanence and uniform boundedness, and the existence of ergodic stationary distribution for the phytoplankton and fish. Ecologically, via numerical analysis, we find that (1) the small random environmental fluctuations can ensure the persistence of phytoplankton and fish, but the larger one can result in the extinction of these populations; (2) an appropriate increase in harvest rate can reduce the irregular random variation of phytoplankton and fish; (3) the increase of toxin liberate rate is capable to decrease the height of probability density function of phytoplankton. These results may help us to better understand the phytoplankton–fish dynamics.

show abstract

“…Upadhyay and Tiwari [15] deeply studied the factors responsible for optimizing economic gain. The authors suggest that optimal harvesting policy can be best chosen only if one understands dynamical features of the concerned ecological system.…”

mentioning

confidence: 99%

Stability analysis and optimal impulsive harvesting for a delayed stage-structured self dependent two compartment commercial fishery model

Sharma

Gupta

Dhar

et al. 2021

Int. J. Dynam. Control

View full text Add to dashboard Cite

Due to overexploitation of renewable resources, we have observed that some species are already extinct. So, the time demands conservation, reproduction and optimal utilization of these resources and the study of such problems. In this paper, a delayed stage-structured self-dependent two compartment (compartment-I contains immature fishes and compartment-II contains mature fishes) commercial fishery model with impulsive harvesting is proposed and analyzed mathematically as well as numerically. The aim is to manage the fishery resource system and that to extract maximum profit without the species become extinct. The proposed system is proved to have positive periodic solutions which are bounded, locally stable and permanent with certain conditions. Then by using optimal impulsive harvesting theory, the optimal harvesting time and optimal harvesting level have been obtained. At last, numerical simulation has been done to support the analytic results, along with comparative plots drawn for different values of harvesting effort E, maturation delay τ and impulsive period T .

show abstract

Ecological chaos and the choice of optimal harvesting policy

Cited by 22 publications

References 53 publications

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Dynamical analysis and optimal harvesting of conformable fractional prey–predator system with predator immigration

Dynamical analysis of a stochastic toxin-producing phytoplankton–fish system with harvesting

Stability analysis and optimal impulsive harvesting for a delayed stage-structured self dependent two compartment commercial fishery model

Contact Info

Product

Resources

About