A Qualitative Study to Strong Allee Effect with Fuzzy Parameters

2015 ◽  
pp. 195-204 ◽  
Author(s):  
Xavier Bertran ◽  
Dolors Corominas ◽  
Narcis Clara
Keyword(s):  
Qualitative Study ◽  
Allee Effect ◽  
Strong Allee Effect ◽  
Fuzzy Parameters

A study of the strong Allee effect with fuzzy parameters for its application in economics

Kybernetes ◽  
2017 ◽  
Vol 46 (1) ◽  
pp. 191-206 ◽  
Author(s):  
Dolors Corominas Coll ◽  
Joan Carles Ferrer-Comalat ◽  
Salvador Linares-Mustarós ◽  
Xavier Bertran
Keyword(s):  
Allee Effect ◽  
Point Of View ◽  
Fuzzy Arithmetic ◽  
Uncertain Environments ◽  
Content Type ◽  
Individual Fitness ◽  
Standard Difference ◽  
Strong Allee Effect ◽  
Low Levels ◽  
Fuzzy Parameters

Purpose The purpose of this study is to present a detailed quantitative and qualitative fuzzy approach to the Allee effect that permits dealing with uncertainty. Design/methodology/approach The Allee effect is related to those aspects of population dynamics that are connected with a decrease in individual fitness when the population size diminishes to very low levels. It allows to model the evolution of certain sectors or clusters which, due to their low population density, may have problems of survival. In uncertain environments, an estimate of the effect’s parameters can be performed in the form of fuzzy numbers, which means that this study is using the methodology of fuzzy arithmetic. Findings This study reveals that fuzziness changes the behavior of the set of solutions when the strong Allee effect is studied under uncertainty from the point of view of standard difference or generalization of the Hukuhara difference. Originality/value The value and originality of the work consists in offering a set of tools for studying the evolution of a group of firms subject to an Allee effect in uncertain environments.

Qualitative analysis of a diffusive predator–prey model with Allee and fear effects

2021 ◽  
pp. 2150037
Author(s):  
Jia Liu
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Allee Effects ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Spatially Homogeneous ◽  
Fear Effects

In this study, we consider a diffusive predator–prey model with multiple Allee effects induced by fear factors. We investigate the existence, boundedness and permanence of the solution of the system. We also discuss the existence and non-existence of non-constant solutions. We derive sufficient conditions for spatially homogeneous (non-homogenous) Hopf bifurcation and steady state bifurcation. Theoretical and numerical simulations show that strong Allee effect and fear effect have great effect on the dynamics of system.

scholarly journals The Role of Dispersal in Interacting Patches Subject to an Allee Effect

2013 ◽  
Vol 45 (4) ◽  
pp. 1182-1197
Author(s):  
N. Lanchier
Keyword(s):  
Allee Effect ◽  
Interacting Particle Systems ◽  
Local Population ◽  
Critical Value ◽  
Initial Distribution ◽  
Interacting Particle ◽  
Strong Allee Effect ◽  
Long Term Behavior

This article is concerned with a stochastic multipatch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch model that was recently introduced by Kang and the author. The main objective is to understand the effect of the geometry of the network of interactions, which represents potential migrations between patches, on the long-term behavior of the metapopulation. In the limit as the number of patches tends to ∞, there is a critical value for the Allee threshold below which the metapopulation expands and above which the metapopulation goes extinct. Spatial simulations on large regular graphs suggest that this critical value strongly depends on the initial distribution when the degree of the network is large, whereas the critical value does not depend on the initial distribution when the degree is small. Looking at the system starting with a single occupied patch on the complete graph and on the ring, we prove analytical results that support this conjecture. From an ecological perspective, these results indicate that, upon arrival of an alien species subject to a strong Allee effect to a new area, though dispersal is necessary for its expansion, fast long-range dispersal drives the population toward extinction.

scholarly journals Stability and Bifurcation in a Predator–Prey Model with the Additive Allee Effect and the Fear Effect

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1280
Author(s):  
Liyun Lai ◽  
Zhenliang Zhu ◽  
Fengde Chen
Keyword(s):  
Allee Effect ◽  
Sufficient Conditions ◽  
Positive Equilibrium ◽  
Predator Species ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Fear Effect ◽  
Prey Model ◽  
Strong Allee Effect ◽  
Theoretical Results

We proposed and analyzed a predator–prey model with both the additive Allee effect and the fear effect in the prey. Firstly, we studied the existence and local stability of equilibria. Some sufficient conditions on the global stability of the positive equilibrium were established by applying the Dulac theorem. Those results indicate that some bifurcations occur. We then confirmed the occurrence of saddle-node bifurcation, transcritical bifurcation, and Hopf bifurcation. Those theoretical results were demonstrated with numerical simulations. In the bifurcation analysis, we only considered the effect of the strong Allee effect. Finally, we found that the stronger the fear effect, the smaller the density of predator species. However, the fear effect has no influence on the final density of the prey.

Von Bertalanffy's growth dynamics with strong Allee effect

2012 ◽  
Vol 32 (1-2) ◽  
pp. 35
Author(s):  
Sandra M. Aleixo ◽  
J. Leonel Rocha
Keyword(s):  
Allee Effect ◽  
Growth Dynamics ◽  
Strong Allee Effect
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