scholarly journals On the Stability of Equilibria in Replicator Dynamics Modelling: An Application in Industrial Dynamics Considering Resource Constraints

2008 ◽  
Author(s):  
Torben Klarl
Keyword(s):  
Resource Constraints ◽  
Replicator Dynamics ◽  
Industrial Dynamics ◽  
Stability Of Equilibria ◽  
Dynamics Modelling ◽  
The Stability

scholarly journals Joint Optimization for Task Offloading in Edge Computing: An Evolutionary Game Approach

Sensors ◽  
2019 ◽  
Vol 19 (3) ◽  
pp. 740 ◽  
Author(s):  
Chongwu Dong ◽  
Wushao Wen
Keyword(s):  
Resource Competition ◽  
Resource Constraints ◽  
Service Providers ◽  
Replicator Dynamics ◽  
Evolutionary Game ◽  
Edge Computing ◽  
Alternative Methods ◽  
The Stability ◽  
Decentralized Resource Allocation ◽  
Task Offloading

The mobile edge computing (MEC) paradigm provides a promising solution to solve the resource-insufficiency problem in mobile terminals by offloading computation-intensive and delay-sensitive tasks to nearby edge nodes. However, limited computation resources in edge nodes may not be sufficient to serve excessive offloading tasks exceeding the computation capacities of edge nodes. Therefore, multiple edge clouds with a complementary central cloud coordinated to serve users is the efficient architecture to satisfy users’ Quality-of-Service (QoS) requirements while trying to minimize some network service providers’ cost. We study a dynamic, decentralized resource-allocation strategy based on evolutionary game theory to deal with task offloading to multiple heterogeneous edge nodes and central clouds among multi-users. In our strategy, the resource competition among multi-users is modeled by the process of replicator dynamics. During the process, our strategy can achieve one evolutionary equilibrium, meeting users’ QoS requirements under resource constraints of edge nodes. The stability and fairness of this strategy is also proved by mathematical analysis. Illustrative studies show the effectiveness of our proposed strategy, outperforming other alternative methods.

Evolutionary Stable Strategies for Supply Chains: Selfishness, Fairness, and Altruism

2018 ◽  
Vol 6 (6) ◽  
pp. 532-551 ◽  
Author(s):  
Caichun Chai ◽  
Hailong Zhu ◽  
Zhangwei Feng
Keyword(s):  
Supply Chains ◽  
Evolutionary Dynamics ◽  
Replicator Dynamics ◽  
Management Strategies ◽  
Individual Preference ◽  
Short Term ◽  
Evolutionary Stable Strategies ◽  
Pure Strategies ◽  
The Stability

Abstract The management strategies of a firm are inevitable affected by individual behavior preferences. The effect of individual preference on the evolutionary dynamics for supply chains is studied by employing replicator dynamics. Each firm has three behavior preferences: selfishness, fairness, and altruism. Firstly, the case that the strategy set of manufacturers and retailers including two pure strategies is considered and the effect of preference parameter on the equilibrium outcome in the short-term interaction is discussed. Secondly, the equilibrium state in the short-term is always disturbed because the change of the environment, firm’s structure, and so forth. Using the replicator dynamics, the evolutionary stable strategies of manufacturers and retailers in the long-term interaction are analyzed. Finally, the extend case that the strategy set of manufacturers and retailers include three pure strategies is investigated. These results are found that the strategy profile in which both manufacturer and retailer choose fairness or altruism, or one player chooses fair or altruistic strategy and the other player chooses selfish strategy may be evolutionary stable, the stability of these equilibria depends on the the preference parameters.

scholarly journals ANALYTICAL APPROACH TO BIT-STRING MODELS OF LANGUAGE EVOLUTION

2008 ◽  
Vol 19 (04) ◽  
pp. 569-581 ◽  
Author(s):  
DAMIÁN H. ZANETTE
Keyword(s):  
Analytical Approach ◽  
Diffusion Processes ◽  
Language Evolution ◽  
Replicator Dynamics ◽  
Mean Field ◽  
Homogeneous State ◽  
Numerical Resolution ◽  
The Stability ◽  
String Models ◽  
And Diffusion

A formulation of bit-string models of language evolution, based on differential equations for the population speaking each language, is introduced and preliminarily studied. Connections with replicator dynamics and diffusion processes are pointed out. The stability of the dominance state, where most of the population speaks a single language, is analyzed within a mean-field-like approximation, while the homogeneous state, where the population is evenly distributed among languages, can be studied. This analysis discloses the existence of a bistability region, where dominance coexists with homogeneity as possible asymptotic states. Numerical resolution of the differential system validates these findings.

Stability and Bifurcation in an SI Epidemic Model with Additive Allee Effect and Time Delay

2021 ◽  
Vol 31 (04) ◽  
pp. 2150060
Author(s):  
Yangyang Lv ◽  
Lijuan Chen ◽  
Fengde Chen ◽  
Zhong Li
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Epidemic Model ◽  
Existence And Uniqueness ◽  
Allee Effect ◽  
Stability Of Equilibria ◽  
Existence And Stability ◽  
Vital Effects ◽  
Strong Allee Effect ◽  
The Stability

In this paper, we consider an SI epidemic model incorporating additive Allee effect and time delay. The primary purpose of this paper is to study the dynamics of the above system. Firstly, for the model without time delay, we demonstrate the existence and stability of equilibria for three different cases, i.e. with weak Allee effect, with strong Allee effect, and in the critical case. We also investigate the existence and uniqueness of Hopf bifurcation and limit cycle. Secondly, for the model with time delay, the stability of equilibria and the existence of Hopf bifurcation are discussed. All the above show that both additive Allee effect and time delay have vital effects on the prevalence of the disease.

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