scholarly journals Stability and Selective Harvesting of a Phytoplankton-Zooplankton System

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yong Wang ◽  
Hongbin Wang
Keyword(s):  
Hopf Bifurcation ◽  
Carrying Capacity ◽  
Optimal Harvesting ◽  
Control Constraints ◽  
State Equations ◽  
Optimal Harvest ◽  
Transcritical Bifurcations ◽  
Bodies Of Water ◽  
The Impact ◽  
Optimal Harvest Policy

Considering that some zooplankton can be harvested for food in some bodies of water, a phytoplankton-zooplankton model with continuous harvesting of zooplankton only is proposed and investigated. By using environmental carrying capacity as a parameter, possible dynamic behaviors, such as stability, global stability, Hopf bifurcation, and transcritical bifurcations, are analyzed. The optimal harvesting policy is disposed by imposing a tax per unit biomass of zooplankton. The problem of determining the optimal harvest policy is solved by using Pontryagin's maximum principle subject to the state equations and the control constraints, and the impact of tax is also discussed. Finally, some numerical simulations are performed to justify analytical findings.

Optimal harvesting of a prey–predator model with variable carrying capacity

2017 ◽  
Vol 10 (05) ◽  
pp. 1750069 ◽  
Author(s):  
Chaity Ganguli ◽  
T. K. Kar ◽  
P. K. Mondal
Keyword(s):  
Carrying Capacity ◽  
Intraspecific Competition ◽  
Dynamical Behavior ◽  
Optimal Harvesting ◽  
Main Concern ◽  
Interior Equilibrium ◽  
Optimal Harvest ◽  
Common Resource ◽  
Predator Model ◽  
Optimal Harvest Policy

This work deals with a prey–predator model in an environment where the carrying capacities are assumed to be variable with time and one species feeds upon the other. Independent harvesting efforts are applied in either species and asymmetrical intraguild predation occurs. A common resource is consumed by two competing species and at the same time predator also consumes the prey. At first we discuss the model under constant carrying capacity and make the conclusion that no limit cycle exists in this case. Then we discuss the model without intraspecific competition. Our main concern is to cover the above mentioned two cases together, i.e. the model with variable carrying capacity and intraspecific competition. We determine the steady states and examine the dynamical behavior. We also analyze the local and global stability of the interior equilibrium by Routh–Hurwitz criterion and a suitable Lyapunov function respectively. A Hopf bifurcation occurs with respect to a parameter which is the ratio of predator’s and prey’s intrinsic growth rate. The possibility of bionomic equilibrium has been considered. The optimal harvest policy is formulated and solved with Pontryagin’s maximum principle. Some numerical simulations are given to explain most of the analytical results.

Bifurcation analysis in a stage-structured predator–prey model with maturation delay

2014 ◽  
Vol 07 (04) ◽  
pp. 1450042
Author(s):  
Jia Liu
Keyword(s):  
Hopf Bifurcation ◽  
Periodic Solutions ◽  
Carrying Capacity ◽  
Positive Equilibrium ◽  
Equilibrium Solutions ◽  
Predator Prey ◽  
Maturation Delay ◽  
Predator Prey Model ◽  
The Stability ◽  
The Impact

In this paper, we investigate the impact of maturation delay on the positive equilibrium solutions in a stage-structured predator–prey system. By analyzing the characteristic equation we derive the conditions for the emergence of Hopf bifurcation. By applying the normal form and the center manifold argument, the direction as well as the stability of periodic solutions bifurcating from Hopf bifurcation is explored. Results show that maturation delay can change the nature of the positive equilibrium solutions, and the loss of equilibrium stability occurs as a consequence of Hopf bifurcation. When Hopf bifurcation takes place, periodic solution arises and is further demonstrated to be asymptotically stable. In addition, the periodic solutions appear only for intermediate maturation delay, that is, there exists a delay window, outside of which the positive equilibrium is locally stable. Furthermore, numerical analysis shows that Hopf bifurcation is favored by a superior competition for adult predators to juveniles, a smaller mortality on juvenile and/or adult predators, and a higher resource carrying capacity. Interestingly, increasing food carrying capacity can lead to the emergence of irregular chaotic dynamics and regular limit cycles.

scholarly journals Dynamics Analysis and Optimality in Selective Harvesting Predator-Prey Model With Modified Leslie-Gower and Holling-Type II

2019 ◽  
Vol 6 (1) ◽  
pp. 1-17
Author(s):  
W. Abid ◽  
R. Yafia ◽  
M. A. Aziz-Alaoui ◽  
Ahmed Aghriche
Keyword(s):  
Existence Of Solutions ◽  
Optimal Harvesting ◽  
Predator Prey ◽  
Interior Equilibrium ◽  
Predator Prey Model ◽  
Optimal Harvest ◽  
Predator Model ◽  
Maximal Principle ◽  
Theoretical Results ◽  
Optimal Harvest Policy

AbstractIn this work, we consider the optimal harvesting and stability problems of a prey-predator model with modified Leslie-Gower and Holling-type II functional response. The model is governed by a system of three differential equations which describe the interactions between prey, predator and harvesting effort. Boundedness and existence of solutions for this system are showed. The existence and local stability of the possible steady states are analyzed and the conditions of global stability of the interior equilibrium are established by using the Lyapunov function, we prove also the occurrence of Hopf bifurcation at this point. By using the Pontryagin’s maximal principle, we formulate and we solve the problem of the optimal harvest policy. In the end, some numerical simulations are given to support our theoretical results.

scholarly journals Understanding drivers of wild oyster population persistence

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mickael Teixeira Alves ◽  
Nick G. H. Taylor ◽  
Hannah J. Tidbury
Keyword(s):  
Population Density ◽  
Carrying Capacity ◽  
Pacific Oyster ◽  
Wild Population ◽  
Population Persistence ◽  
Oyster Reefs ◽  
Oyster Population ◽  
Northern European ◽  
Age Structured ◽  
The Impact

AbstractPersistence of wild Pacific oyster, Magallana gigas, also known as Crassostrea gigas, has been increasingly reported across Northern European waters in recent years. While reproduction is inhibited by cold waters, recent warm summer temperature has increased the frequency of spawning events. Although correlation between the increasing abundance of Pacific oyster reefs in Northern European waters and climate change is documented, persistence of wild populations may also be influenced by external recruitment from farmed populations and other wild oyster populations, as well as on competition for resources with aquaculture sites. Our understanding of the combined impact of the spawning frequency, external recruitment, and competition on wild population persistence is limited. This study applied an age-structured model, based on ordinary differential equations, to describe an oyster population under discrete temperature-related dynamics. The impact of more frequent spawning events, external recruitment, and changes in carrying capacity on Pacific oyster density were simulated and compared under theoretical scenarios and two case studies in Southern England. Results indicate that long term persistence of wild oyster populations towards carrying capacity requires a high frequency of spawning events but that in the absence of spawning, external recruitment from farmed populations and other wild oyster populations may act to prevent extinction and increase population density. However, external recruitment sources may be in competition with the wild population so that external recruitment is associated with a reduction in wild population density. The implications of model results are discussed in the context of wild oyster population management.

scholarly journals Quantifying the Impact of Mounted Load Carrying on Equids: A Review

Animals ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1333
Author(s):  
Syed S. U. H. Bukhari ◽  
Alan G. McElligott ◽  
Rebecca S. V. Parkes
Keyword(s):  
Carrying Capacity ◽  
Creatine Kinase Activity ◽  
Serum Cortisol Level ◽  
Load Carrying Capacity ◽  
Gait Symmetry ◽  
Brick Kilns ◽  
Potential Marker ◽  
Load Carrying ◽  
The Impact ◽  
Working Equids

There are approximately 112 million working equids in developing countries, many of which are associated with brick kilns. Brick kilns and overloading are associated with welfare problems in working equids. Understanding equids’ abilities and influencing factors are important for both effective performance and welfare. Traditionally, measurement of the amount of ‘bone’ was used, and more recently, gait symmetry has been identified as a potential marker for loading capacity. Assessment of stride parameters and gait kinematics provides insights into adaptations to loading and may help determine cut-off loads. Physiological factors such as the ability to regain normal heart rates shortly after work is an important tool for equine fitness assessment and a more accurate measure of load-carrying capacity than absolute heart rate. Oxidative stress, plasma lactate, and serum creatine kinase activity are reliable biochemical indicators of loading ability. For monitoring stress, salivary cortisol is superior to serum cortisol level for assessment of hypothalamus-pituitary-adrenal axis and is related to eye temperatures, but this has yet to be interpreted in terms of load-carrying ability in equids. Further research is needed to standardize the evidence-based load-carrying capacity of working horses and donkeys.

Changes in Ecosystems of Bodies of Water Resulting from of the Aaggregates Extraction

2021 ◽  
Vol 25 (9) ◽  
pp. 44-49
Author(s):  
S.S. Uskova
Keyword(s):  
Food Supply ◽  
Small Body ◽  
Large Body ◽  
Small Rivers ◽  
Complete Destruction ◽  
Research Findings ◽  
Downstream Flow ◽  
Bodies Of Water ◽  
The Impact ◽  
Lower Capacity

The evaluation issues on the aggregate’s extraction on the ecosystem of bodies of water has been considered. The dredgers' impact of various capacities on bodies of water of different capacities have been compared, as well as on food supply change of bodies of water for benthos eater. The research findings have showed the dragger's impact of a higher capacity is bigger on a large body of water than this of a lower capacity on a small body of water. The impact manifests itself in decreasing the number and biomass of macrozoobenthos in the area used for the oil and lubricants extraction and the downstream flow. It has been found that the complete destruction of macrozoobenthos at the site of hydraulic engineering activities has not been detected either in small rivers or in large reservoirs.

scholarly journals Spatial Pattern Analysis of a Water-Related Ecosystem Service and Evaluation of the Grassland-Carrying Capacity of the Heihe River Basin under Land Use Change

Water ◽  
2021 ◽  
Vol 13 (19) ◽  
pp. 2658
Author(s):  
Rui Luo ◽  
Shiliang Yang ◽  
Yang Zhou ◽  
Pengqun Gao ◽  
Tianming Zhang
Keyword(s):  
Land Use ◽  
Ecosystem Services ◽  
Land Use Change ◽  
River Basin ◽  
Carrying Capacity ◽  
Animal Husbandry ◽  
Heihe River Basin ◽  
Heihe River ◽  
The Impact ◽  
The Heihe River Basin

A key challenge to the sustainability and security of grassland capacity is the protection of water-related ecosystem services (WESs). With the change of land use, the supply of aquatic ecosystem services has changed, and the grassland-carrying capacity has been affected. However, the correlation mechanism between WESs and the grassland-carrying capacity is not clear. In this study, we used the InVEST(Integrated Valuation of Ecosystem Services and Tradeoffs) model to evaluate the impact of land-use change on WESs, and made a tradeoff analysis between WESs and grassland-carrying capacity. Considering that the Heihe River Basin (HRB) was an important grassland vegetation zone, which was a milestone for the development of animal husbandry in China, HRB was taken as a case. The main findings are as follows: (1) the spatial distribution of WESs shows the dissimilation rule, the upper reaches are the main water yield area, the soil retention is weakening in the middle and lower reaches, and the pollution has further increased in the middle and upper reaches. (2) The carrying capacity of animal husbandry decreased in the upper reaches, increased in Shandan County and Zhangye City in the middle reaches, and decreased sharply in other regions. (3) There was a positive correlation between the livestock-carrying capacity and nitrogen export in 2018, which was increasing. As the change of land use has changed the evapotranspiration structure, WESs have undergone irreversible changes. Meanwhile, the development of large-scale irrigated farmland and human activities would be the source of a further intensification of regional soil erosion and water pollution. Therefore, it is necessary to trade off the WESs and animal husbandry under land-use change. This paper revealed how WESs changed from 2000 to 2018, the characteristics of the changes in the spatial and temporal distribution, and the carrying capacity. It aims to provide a scientific basis for coordinating the contradiction between grassland and livestock resources, improving the regional ecological security situation, and carrying out ecosystem management.

scholarly journals Decision making of maritime development scenario on the impact of naval base for supporting navy ships operations

2022 ◽  
Vol 11 (1) ◽  
pp. 81-90 ◽  
Author(s):  
Okol Sri Suharyo ◽  
Ayip Rivai Prabowo ◽  
Eko Krisdiono
Keyword(s):  
Carrying Capacity ◽  
Development Program ◽  
Dynamics Modeling ◽  
Port Security ◽  
Support Functions ◽  
Port Development ◽  
Development Scenarios ◽  
Facility Maintenance ◽  
The Impact ◽  
Naval Base

The Indonesian Navy is the spearhead in maintaining maritime security in Indonesian waters. In carrying out its main tasks, the Indonesian Navy has components of an Integrated Fleet Weapon System in which there are elements of Ships and Naval Bases. To ensure the effectiveness of carrying out operations by ship elements, ship operations are supported by the Naval Base as the organizer of the support function. Naval Base's carrying capacity consists of 5 (five) support functions, including: (1) support for anchoring facilities; (2) support for supply facilities; (3) support for maintenance and repair facilities; (4) support facility maintenance personnel; and (5) support for base development facilities. Naval Base does not yet have its dock to support anchoring facilities for ship operations. In addition to cooperation in the use of the Naval Base anchorage facility, there is also cooperation in port security, both in terms of land and port water aspects. As the number of ship visits at Naval Base Harbor increases, the dock utility increases. The increase in dock utility resulted in a decrease in port services which also resulted in a decrease in the Naval Base Carrying Capacity. To improve port services, Pelindo III implements the port development program contained in the Naval Base Port Master Plan in Permen KP number 792 of 2017. In this study, an analysis of the impact of the Naval Base Port development policy on the carrying capacity of the Naval Base was carried out. The data analysis uses System Dynamics modeling with a simulation period of 30 years in 3 development scenarios, namely short-term scenarios, medium-term scenarios, and long-term scenarios. From the simulation results, it is found that the construction of the Naval Base port affects the Naval Base Carrying Capacity with an average increase of 1.8% in each policy scenario. The increase in Naval Base Carrying Capacity has an effect on increasing Ship Operations by an average of 1.8% and also increasing the Security of Naval Base Harbor by an average of 0.14%. The results of the analysis of this study can be used as consideration for policymaking by the Navy.

scholarly journals A STUDY OF FERROFLUID LUBRICATION BASED ROUGH SINE FILM SLIDER BEARING WITH ASSORTED POROUS STRUCTURE

2019 ◽  
Vol 59 (2) ◽  
pp. 144-152
Author(s):  
Mohmmadraiyan M. Munshi ◽  
Ashok R. Patel ◽  
Gunamani B. Deheri
Keyword(s):  
Porous Structure ◽  
Carrying Capacity ◽  
Graphical Representation ◽  
Negative Impact ◽  
Positive Impact ◽  
Numerical Approach ◽  
Load Carrying Capacity ◽  
Slider Bearing ◽  
Load Carrying ◽  
The Impact

This paper attempts to study a ferrofluid lubrication based rough sine film slider bearing with assorted porous structure using a numerical approach. The fluid flow of the system is regulated by the Neuringer-Rosensweig model. The impact of the transverse surface roughness of the system has been derived using the Christensen and Tonder model. The corresponding Reynolds’ equation has been used to calculate the pressure distribution which, in turn, has been the key to formulate the load carrying capacity equation. A graphical representation is made to demonstrate the calculated value of the load carrying capacity which is a dimensionless unit. The numbers thus derived have been used to prove that ferrofluid lubrication aids the load carrying capacity. The study suggests that the positive impact created by magnetization in the case of negatively skewed roughness helps to partially nullify the negative impact of the transverse roughness. Further investigation implies that when the Kozeny-Carman’s model is used, the overall performance is enhanced. The Kozeny-Carman’s model is a form of an empirical equation used to calculate permeability that is dependent on various parameters like pore shape, turtuosity, specific surface area and porosity. The success of the model can be accredited to its simplicity and efficiency to describe measured permeability values. The obtained equation was used to predict the permeability of fibre mat systems and of vesicular rocks.

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