Allee Effect in Prey versus Hunting Cooperation on Predator — Enhancement of Stable Coexistence

2019 ◽  
Vol 29 (06) ◽  
pp. 1950081 ◽  
Author(s):  
Deeptajyoti Sen ◽  
S. Ghorai ◽  
Malay Banerjee
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Allee Effect ◽  
Interaction Model ◽  
Type Model ◽  
Predator Density ◽  
Predator Foraging ◽  
The Stability ◽  
Generalized Type ◽  
Type Ii Functional Response

Predator foraging facilitation or cooperative hunting increases per predator consumption rate as predator density increases. This affects predator extinction in a prey–predator interaction model when the predator density is low. This is an indication of Allee effect in predator’s growth rate. Here, we take a Gause type model with a generalized type II functional response which depends on both prey and predator densities. We also assume that prey’s growth is subjected to Allee effect. Strong Allee effect in prey’s growth rate enhances the stability of the coexisting steady state. A region is found in a two-parameter plane where the coexisting steady state is a global attractor when the prey’s growth is subjected to weak Allee effect. In addition, codimension two bifurcation points (cusp and Bogdanov–Takens points) have also been found in the bifurcation diagram.

Dynamics and pattern formation in a modified Leslie–Gower model with Allee effect and Bazykin functional response

2017 ◽  
Vol 10 (05) ◽  
pp. 1750073 ◽  
Author(s):  
Peng Feng
Keyword(s):  
Steady State ◽  
Pattern Formation ◽  
Spatial Pattern ◽  
Numerical Simulations ◽  
Functional Response ◽  
Allee Effect ◽  
Turing Instability ◽  
Spatial Pattern Formation ◽  
The Stability ◽  
Steady State Solutions

In this paper, we study the dynamics of a diffusive modified Leslie–Gower model with the multiplicative Allee effect and Bazykin functional response. We give detailed study on the stability of equilibria. Non-existence of non-constant positive steady state solutions are shown to identify the rage of parameters of spatial pattern formation. We also give the conditions of Turing instability and perform a series of numerical simulations and find that the model exhibits complex patterns.

scholarly journals Computational Analysis of the Properties of Post-Keynesian Endogenous Money Systems

2021 ◽  
Vol 14 (7) ◽  
pp. 335
Author(s):  
Stef Kuypers ◽  
Thomas Goorden ◽  
Bruno Delepierre
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Real World ◽  
Money Stock ◽  
Monetary System ◽  
Monetary Systems ◽  
State Economy ◽  
Endogenous Money ◽  
New Perspective ◽  
The Stability

The debate about whether or not a growth imperative exists in debt-based, interest-bearing monetary systems has not yet been settled. It is the goal of this paper to introduce a new perspective in this discussion. For that purpose, an SFC computational model is constructed that simulates a post-Keynesian endogenous money system without including economic parameters such as production, wages, consumption and savings. The case is made that isolating the monetary system allows for better analysis of the inherent properties of such a system. Loan demands, which are assumed to happen, are the driving force of the model. Simulations can be run in two modes, each based on a different assumption. Either the growth rate of the money stock is assumed to be constant or the loan ratio, expressed as a percentage of the money stock, is assumed to be constant. Simulations with varying parameters were run in order to determine the conditions under which the model converges to stability, which is defined as converging to a bounded debt ratio. The analysis showed that the stability of the model is dependent on net bank profit ratios, expressed relative to their debt assets, remaining below the growth rate of the money stock. Based on these findings, it is argued that the question about the existence of a growth imperative in debt-based, interest-bearing monetary systems needs to be reframed. The question becomes whether a steady-state economy can realistically support such a system without destabilising it. In order to answer this question, the real-world behaviour of economic actors must be included in the model. It was concluded that there are indications that it might not be feasible for a steady-state economy to support a stable debt-based, interest-bearing monetary system without strong interventions. However, more research is necessary for a definite answer. Real-world observable data should be analysed through the lens of the presented model to bring more clarity.

scholarly journals Polyamine, Magnesium and Ribonucleic Acid Levels in Steady-state Cultures of the Mould Aspergillus nidulans

Microbiology ◽  
2000 ◽  
Vol 81 (1) ◽  
pp. 271-273 ◽  
Author(s):  
M. E. Bushell ◽  
A. T. Bull
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Aspergillus Nidulans ◽  
Culture Conditions ◽  
Magnesium Ions ◽  
Ribonucleic Acids ◽  
Inorganic Cations ◽  
State Growth ◽  
The Stability ◽  
Cell Free Protein Synthesis

Results from experiments in vitro strongly suggest that major roles can be ascribed to polyamines in controlling the stability, activity and synthesis of ribonucleic acids. Furthermore, functional substitution of polyamines for inorganic cations, particularly magnesium ions, in cell-free protein synthesis is well substantiated (see Cohen, 1971). Recently we have been analysing the effects of culture conditions on the chemical composition of Aspergillus nidulans and have found fluctuations in polyamine and magnesium concentrations in response to a changing environment, while biomass and RNA remained constant. This paper describes the influence of steady-state growth rate on hyphal concentrations of spermidine, spermine and Mg2+ ions.

Reexamination of the Serendipity Theorem from the stability viewpoint

2019 ◽  
Vol 85 (1) ◽  
pp. 43-70
Author(s):  
Akira Momota ◽  
Tomoya Sakagami ◽  
Akihisa Shibata
Keyword(s):  
Growth Rate ◽  
Steady State ◽  
Population Growth ◽  
Numerical Simulations ◽  
Policy Implication ◽  
Population Growth Rate ◽  
Golden Rule ◽  
The Social ◽  
The Stability ◽  
Parameter Values

AbstractThis paper reexamines the Serendipity Theorem of Samuelson (1975) from the stability viewpoint, and shows that, for the Cobb–Douglas preference and CES technology, the most-golden golden-rule lifetime state being stable depends on parameter values. In some situations, the Serendipity Theorem fails to hold despite the fact that steady-state welfare is maximized at the population growth rate, since the steady state is unstable. Through numerical simulations, a more general case of CES preference and CES technology is also examined, and we discuss the realistic relevance of our results. We present the policy implication of our result, that is, in some cases, the steady state with the highest utility is unstable, and thus a policy that aims to achieve the social optima by manipulating the population growth rate may lead to worse outcomes.

The Stability of Steady-State Depth Distributions of Marine Phytoplankton

1974 ◽  
Vol 108 (963) ◽  
pp. 679-687 ◽  
Author(s):  
W. O. Criminale, ◽  
D. F. Winter
Keyword(s):  
Steady State ◽  
Marine Phytoplankton ◽  
The Stability ◽  
Depth Distributions

scholarly journals Steady-state $$\dot{V}{\text{O}}_{2}$$ above MLSS: evidence that critical speed better represents maximal metabolic steady state in well-trained runners

2021 ◽  
Author(s):  
Rebekah J. Nixon ◽  
Sascha H. Kranen ◽  
Anni Vanhatalo ◽  
Andrew M. Jones
Keyword(s):  
Steady State ◽  
Critical Speed ◽  
Lactate Concentration ◽  
Practical Interest ◽  
Blood Lactate Concentration ◽  
Distance Runners ◽  
Severe Intensity ◽  
The Stability ◽  
Trained Runners ◽  
Over Time

AbstractThe metabolic boundary separating the heavy-intensity and severe-intensity exercise domains is of scientific and practical interest but there is controversy concerning whether the maximal lactate steady state (MLSS) or critical power (synonymous with critical speed, CS) better represents this boundary. We measured the running speeds at MLSS and CS and investigated their ability to discriminate speeds at which $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 was stable over time from speeds at which a steady-state $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 could not be established. Ten well-trained male distance runners completed 9–12 constant-speed treadmill tests, including 3–5 runs of up to 30-min duration for the assessment of MLSS and at least 4 runs performed to the limit of tolerance for assessment of CS. The running speeds at CS and MLSS were significantly different (16.4 ± 1.3 vs. 15.2 ± 0.9 km/h, respectively; P < 0.001). Blood lactate concentration was higher and increased with time at a speed 0.5 km/h higher than MLSS compared to MLSS (P < 0.01); however, pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 did not change significantly between 10 and 30 min at either MLSS or MLSS + 0.5 km/h. In contrast, $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 increased significantly over time and reached $$\dot{V}{\text{O}}_{2\,\,\max }$$ V ˙ O 2 max at end-exercise at a speed ~ 0.4 km/h above CS (P < 0.05) but remained stable at a speed ~ 0.5 km/h below CS. The stability of $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 at a speed exceeding MLSS suggests that MLSS underestimates the maximal metabolic steady state. These results indicate that CS more closely represents the maximal metabolic steady state when the latter is appropriately defined according to the ability to stabilise pulmonary $$\dot{V}{\text{O}}_{2}$$ V ˙ O 2 .

Stability of bounded rapid shear flows of a granular material

1996 ◽  
Vol 308 ◽  
pp. 31-62 ◽  
Author(s):  
Chi-Hwa Wang ◽  
R. Jackson ◽  
S. Sundaresan
Keyword(s):  
Growth Rate ◽  
Stability Analysis ◽  
Granular Material ◽  
Bulk Density ◽  
Particulate Material ◽  
Dominant Mode ◽  
Marginal Stability ◽  
Sheared Layer ◽  
The Stability ◽  
Unusual Type

This paper presents a linear stability analysis of a rapidly sheared layer of granular material confined between two parallel solid plates. The form of the steady base-state solution depends on the nature of the interaction between the material and the bounding plates and three cases are considered, in which the boundaries act as sources or sinks of pseudo-thermal energy, or merely confine the material while leaving the velocity profile linear, as in unbounded shear. The stability analysis is conventional, though complicated, and the results are similar in all cases. For given physical properties of the particles and the bounding plates it is found that the condition of marginal stability depends only on the separation between the plates and the mean bulk density of the particulate material contained between them. The system is stable when the thickness of the layer is sufficiently small, but if the thickness is increased it becomes unstable, and initially the fastest growing mode is analogous to modes of the corresponding unbounded problem. However, with a further increase in thickness a new mode becomes dominant and this is of an unusual type, with no analogue in the case of unbounded shear. The growth rate of this mode passes through a maximum at a certain value of the thickness of the sheared layer, at which point it grows much faster than any mode that could be shared with the unbounded problem. The growth rate of the dominant mode also depends on the bulk density of the material, and is greatest when this is neither very large nor very small.

scholarly journals The influence of density in population dynamics with strong and weak Allee effect

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
Kamrun Nahar Keya ◽  
Md. Kamrujjaman ◽  
Md. Shafiqul Islam
Keyword(s):  
Population Dynamics ◽  
Allee Effect ◽  
Global Bifurcation ◽  
Reaction Diffusion ◽  
Logistic Growth ◽  
Allee Effects ◽  
Reaction Diffusion Model ◽  
Positive Steady States ◽  
The Stability ◽  
The Impact

AbstractIn this paper, we consider a reaction–diffusion model in population dynamics and study the impact of different types of Allee effects with logistic growth in the heterogeneous closed region. For strong Allee effects, usually, species unconditionally die out and an extinction-survival situation occurs when the effect is weak according to the resource and sparse functions. In particular, we study the impact of the multiplicative Allee effect in classical diffusion when the sparsity is either positive or negative. Negative sparsity implies a weak Allee effect, and the population survives in some domain and diverges otherwise. Positive sparsity gives a strong Allee effect, and the population extinct without any condition. The influence of Allee effects on the existence and persistence of positive steady states as well as global bifurcation diagrams is presented. The method of sub-super solutions is used for analyzing equations. The stability conditions and the region of positive solutions (multiple solutions may exist) are presented. When the diffusion is absent, we consider the model with and without harvesting, which are initial value problems (IVPs) and study the local stability analysis and present bifurcation analysis. We present a number of numerical examples to verify analytical results.

Predator-dependent transmissible disease spreading in prey under Holling type-II functional response

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Dipankar Ghosh ◽  
Prasun K. Santra ◽  
Abdelalim A. Elsadany ◽  
Ghanshaym S. Mahapatra
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Linearization Method ◽  
Logistic Growth ◽  
Type Ii ◽  
Disease Spreading ◽  
Predator Interactions ◽  
The Stability ◽  
Infected Prey ◽  
Type Ii Functional Response

Abstract This paper focusses on developing two species, where only prey species suffers by a contagious disease. We consider the logistic growth rate of the prey population. The interaction between susceptible prey and infected prey with predator is presumed to be ruled by Holling type II and I functional response, respectively. A healthy prey is infected when it comes in direct contact with infected prey, and we also assume that predator-dependent disease spreads within the system. This research reveals that the transmission of this predator-dependent disease can have critical repercussions for the shaping of prey–predator interactions. The solution of the model is examined in relation to survival, uniqueness and boundedness. The positivity, feasibility and the stability conditions of the fixed points of the system are analysed by applying the linearization method and the Jacobian matrix method.

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