scholarly journals Global stability of fuzzy cognitive maps

2021 ◽  
Author(s):  
István Á. Harmati ◽  
Miklós F. Hatwágner ◽  
László T. Kóczy
Keyword(s):  
Fixed Point ◽  
Global Stability ◽  
Cognitive Maps ◽  
Fuzzy Cognitive Maps ◽  
Initial Vector ◽  
Asymptotically Stable ◽  
Global Asymptotical Stability ◽  
Initial State ◽  
Globally Asymptotically Stable ◽  
Multiple Fixed Points

AbstractComplex systems can be effectively modelled by fuzzy cognitive maps. Fuzzy cognitive maps (FCMs) are network-based models, where the connections in the network represent causal relations. The conclusion about the system is based on the limit of the iteratively applied updating process. This iteration may or may not reach an equilibrium state (fixed point). Moreover, if the model is globally asymptotically stable, then this fixed point is unique and the iteration converges to this point from every initial state. There are some FCM models, where global stability is the required property, but in many FCM applications, the preferred scenario is not global stability, but multiple fixed points. Global stability bounds are useful in both cases: they may give a hint about which parameter set should be preferred or avoided. In this article, we present novel conditions for the global asymptotical stability of FCMs, i.e. conditions under which the iteration leads to the same point from every initial vector. Furthermore, we show that the results presented here outperform the results known from the current literature.

scholarly journals Global Stability and Optimal Control of Dengue with Two Coexisting Virus Serotypes

MATEMATIKA ◽  
2019 ◽  
Vol 35 (4) ◽  
pp. 149-170
Author(s):  
Afeez Abidemi ◽  
Rohanin Ahmad ◽  
Nur Arina Bazilah Aziz
Keyword(s):  
Optimal Control ◽  
Global Stability ◽  
Disease Transmission ◽  
Deterministic Model ◽  
Control Strategies ◽  
Equilibrium Points ◽  
Effective Control ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Boundary Equilibrium

This study presents a two-strain deterministic model which incorporates Dengvaxia vaccine and insecticide (adulticide) control strategies to forecast the dynamics of transmission and control of dengue in Madeira Island if there is a new outbreak with a different virus serotypes after the first outbreak in 2012. We construct suitable Lyapunov functions to investigate the global stability of the disease-free and boundary equilibrium points. Qualitative analysis of the model which incorporates time-varying controls with the specific goal of minimizing dengue disease transmission and the costs related to the control implementation by employing the optimal control theory is carried out. Three strategies, namely the use of Dengvaxia vaccine only, application of adulticide only, and the combination of Dengvaxia vaccine and adulticide are considered for the controls implementation. The necessary conditions are derived for the optimal control of dengue. We examine the impacts of the control strategies on the dynamics of infected humans and mosquito population by simulating the optimality system. The disease-freeequilibrium is found to be globally asymptotically stable whenever the basic reproduction numbers associated with virus serotypes 1 and j (j 2 {2, 3, 4}), respectively, satisfy R01,R0j 1, and the boundary equilibrium is globally asymptotically stable when the related R0i (i = 1, j) is above one. It is shown that the strategy based on the combination of Dengvaxia vaccine and adulticide helps in an effective control of dengue spread in the Island.

scholarly journals Global Stability of Malaria Transmission Dynamics Model with Logistic Growth

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Abadi Abay Gebremeskel
Keyword(s):  
Sensitivity Analysis ◽  
Global Stability ◽  
Malaria Transmission ◽  
Equilibrium Points ◽  
Transmission Dynamics ◽  
Logistic Growth ◽  
Asymptotically Stable ◽  
Dynamics Model ◽  
Globally Asymptotically Stable ◽  
The Impact

Mathematical models become an important and popular tools to understand the dynamics of the disease and give an insight to reduce the impact of malaria burden within the community. Thus, this paper aims to apply a mathematical model to study global stability of malaria transmission dynamics model with logistic growth. Analysis of the model applies scaling and sensitivity analysis and sensitivity analysis of the model applied to understand the important parameters in transmission and prevalence of malaria disease. We derive the equilibrium points of the model and investigated their stabilities. The results of our analysis have shown that if R0≤1, then the disease-free equilibrium is globally asymptotically stable, and the disease dies out; if R0>1, then the unique endemic equilibrium point is globally asymptotically stable and the disease persists within the population. Furthermore, numerical simulations in the application of the model showed the abrupt and periodic variations.

FUZZY COGNITIVE MAPS WITH GENETIC ALGORITHM FOR GOAL-ORIENTED DECISION SUPPORT

2004 ◽  
Vol 12 (supp02) ◽  
pp. 31-42 ◽  
Author(s):  
M. SHAMIM KHAN ◽  
SEBASTIAN KHOR ◽  
ALEX CHONG
Keyword(s):  
Genetic Algorithm ◽  
Decision Making ◽  
Genetic Algorithms ◽  
Decision Support ◽  
Directed Graphs ◽  
Cognitive Maps ◽  
Fuzzy Cognitive Maps ◽  
Initial State ◽  
Initial Stimulus ◽  
Over Time

Fuzzy cognitive maps are signed directed graphs used to model the evolution of scenarios with time. FCMs can be useful in decision support for predicting future states given an initial state. Genetic algorithms (GA) are well-established tools for optimization. This paper concerns the use of FCMs in goal-directed analysis of scenarios for aiding decision making. A methodology for GA-based goal-directed analysis is presented. The search for the initial stimulus state, that over time leads to a target state of interest, is optimized using GA. This initial state found can be used to answer the question – what course of events leads to a certain state in a given scenario?

scholarly journals Global Stability of Vector-Host Disease with Variable Population Size

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Saeed Islam ◽  
Sher Afzal Khan ◽  
Gul Zaman
Keyword(s):  
Global Stability ◽  
Population Size ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Host Disease ◽  
Variable Population ◽  
Globally Stable ◽  
Disease Free ◽  
Disease Persistence ◽  
Variable Population Size

The paper presents the vector-host disease with a variability in population. We assume, the disease is fatal and for some cases the infected individuals become susceptible. We first show the local and global stability of the disease-free equilibrium, for the case when, the disease free-equilibrium of the model is both locally as well as globally stable. For , the disease persistence occurs. The endemic equilibrium is locally as well as globally asymptotically stable for . Numerical results are presented for the justifications of theoratical results.

ON THE GLOBAL STABILITY OF CHOLERA MODEL WITH PREVENTION AND CONTROL

2018 ◽  
Vol 3 (1) ◽  
pp. 28
Author(s):  
M O Ibrahim ◽  
A A Ayoade ◽  
O J Peter ◽  
F A Oguntolu
Keyword(s):  
Global Stability ◽  
Prevention And Control ◽  
Control Measures ◽  
Extended Model ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
First Order ◽  
Prevention And Control Measures ◽  
And Control ◽  
Disease Free

In this study, a system of first order ordinary differential equations is used to analyse the dynamics of cholera disease via a mathematical model extended from Fung (2014) cholera model. The global stability analysis is conducted for the extended model by suitable Lyapunov function and LaSalle’s invariance principle. It is shown that the disease free equilibrium (DFE) for the extended model is globally asymptotically stable if 𝑅0 𝑞 < 1 and the disease eventually disappears in the population with time while there exists a unique endemic equilibrium that is globally asymptotically stable whenever 𝑅0 𝑞 > 1 for the extended model or 𝑅0 > 1 for the original model and the disease persists at a positive level though with mild waves (i.e few cases of cholera) in the case of𝑅0 𝑞 > 1. Numerical simulations for strong, weak, and no prevention and control measures are carried out to verify the analytical results and Maple 18 is used to carry out the computations.

scholarly journals Global Stability of a HIV-1 Model with General Nonlinear Incidence and Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Yaping Wang ◽  
Fuqin Sun
Keyword(s):  
Global Stability ◽  
Endemic Equilibrium ◽  
Asymptotically Stable ◽  
Threshold Behavior ◽  
Globally Asymptotically Stable ◽  
Incidence Functions ◽  
The Given ◽  
Disease Free ◽  
Hiv 1 ◽  
Intracellular Delays

A HIV-1 model with two distributed intracellular delays and general incidence function is studied. Conditions are given under which the system exhibits the threshold behavior: the disease-free equilibriumE0is globally asymptotically stable ifR0≤1; ifR0>1, then the unique endemic equilibriumE1is globally asymptotically stable. Finally, it is shown that the given conditions are satisfied by several common forms of the incidence functions.

scholarly journals COVID-19 and digital transformation: developing an open experimental testbed for sustainable and innovative environments using Fuzzy Cognitive Maps

F1000Research ◽  
2021 ◽  
Vol 10 ◽  
pp. 264
Author(s):  
Wolfgang Höhl
Keyword(s):  
Social Impact ◽  
Cognitive Maps ◽  
Digital Transformation ◽  
Fuzzy Cognitive Maps ◽  
Minor Role ◽  
Initial State ◽  
New Approach ◽  
Innovative Environments ◽  
Experimental Testbed ◽  
A Minor

This paper sketches a new approach using Fuzzy Cognitive Maps (FCMs) to operably map and simulate digital transformation in architecture and urban planning. Today these processes are poorly understood. Many current studies on digital transformation are only treating questions of economic efficiency. Sustainability and social impact only play a minor role. Decisive definitions, concepts and terms stay unclear. Therefore this paper develops an open experimental testbed for sustainable and innovative environments (ETSIE) for three different digital transformation scenarios using FCMs. A traditional growth-oriented scenario, a COVID-19 scenario and an innovative and sustainable COVID-19 scenario are modeled and tested. All three scenarios have the same number of components, connections and the same driver components. Only the initial state vectors are different and the internal correlations are weighted differently. This allows for comparing all three scenarios on an equal basis. The Mental Modeler software is used. This paper presents one of the first applications of FCMs in the context of digital transformation. It is shown that the traditional growth-oriented scenario is structurally very similar to the current COVID-19 scenario. The current pandemic is able to accelerate digital transformation to a certain extent. But the pandemic does not guarantee for a distinct sustainable and innovative future development. Only by changing the initial state vectors and the weights of the connections an innovative and sustainable turnaround in a third scenario becomes possible.

Global Stability of a HBV Infection Model with Saturated Infection Rates and Time Delay

2013 ◽  
Vol 791-793 ◽  
pp. 1314-1317
Author(s):  
Wei Juan Pang ◽  
Zhi Xing Hu ◽  
Fu Cheng Liao
Keyword(s):  
Global Stability ◽  
Sufficient Conditions ◽  
Hbv Infection ◽  
Basic Reproductive Number ◽  
Reproductive Number ◽  
Infection Model ◽  
Asymptotically Stable ◽  
Infection Rates ◽  
Globally Asymptotically Stable ◽  
Viral Infection Model

This paper investigates the global stability of a viral infection model of HBV infection of hepatocytes with saturated infection rate and intracellular delay. we obtain if the basic reproductive number is less than or equal to one, the infection-free equilibrium is globally asymptotically stable. If its greater than one, we obtain the sufficient conditions for the global stability of the infected equilibrium.

scholarly journals Global Behavior ofxn+1=(α+βxn-k)/(γ+xn)

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Chenquan Gan ◽  
Xiaofan Yang ◽  
Wanping Liu
Keyword(s):  
Positive Integer ◽  
Difference Equation ◽  
Global Stability ◽  
Initial Conditions ◽  
Global Behavior ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
The Difference

This paper aims to investigate the global stability of negative solutions of the difference equationxn+1=(α+βxn-k)/(γ+xn),n=0,1,2,…, where the initial conditionsx-k,…,x0∈-∞,0,kis a positive integer, and the parametersβ,  γ<0,  α>0. By utilizing the invariant interval and periodic character of solutions, it is found that the unique negative equilibrium is globally asymptotically stable under some parameter conditions. Additionally, two examples are given to illustrate the main results in the end.

scholarly journals Global Stability of an Epidemic Model of Computer Virus

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaofan Yang ◽  
Bei Liu ◽  
Chenquan Gan
Keyword(s):  
Global Stability ◽  
Epidemic Model ◽  
Computer Virus ◽  
Propagation Model ◽  
Parameter Analysis ◽  
The Internet ◽  
Asymptotically Stable ◽  
Unique Equilibrium ◽  
Globally Asymptotically Stable ◽  
Computer Viruses

With the rapid popularization of the Internet, computers can enter or leave the Internet increasingly frequently. In fact, no antivirus software can detect and remove all sorts of computer viruses. This implies that viruses would persist on the Internet. To better understand the spread of computer viruses in these situations, a new propagation model is established and analyzed. The unique equilibrium of the model is globally asymptotically stable, in accordance with the reality. A parameter analysis of the equilibrium is also conducted.

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