Analysis of Chaotic Behavior for the Confliction Model with Fuzzy External Force

In this study, we propose a new confliction model based on the fuzzy theory. The confliction model has developed by a differential equation with an external force as a sinusoidal function in several studies. The confliction model includes two important functions of time, that is confliction status a...

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Bibliographic Details
Published in:International journal of fuzzy systems 2022-06, Vol.24 (4), p.2054-2067
Main Authors: Yoon, Jin Hee, Huang, Linyun, Bae, Young-Chul
Format: Article
Language:English
Subjects:
Ambiguity
Artificial Intelligence
Computational Intelligence
Differential equations
Engineering
Fuzzy sets
Liapunov exponents
Management Science
Numbers
Operations Research
Social sciences
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Summary:In this study, we propose a new confliction model based on the fuzzy theory. The confliction model has developed by a differential equation with an external force as a sinusoidal function in several studies. The confliction model includes two important functions of time, that is confliction status and the external force. However, the degree of conflict or external forces cannot be expressed precisely, so this model does not describe the situation appropriately. Therefore, this paper applies fuzzy theory to this model to describe the vagueness that the degree of confliction or external force has. For this, we observed the chaotic behaviors of the model by varying the values of the parameters. We also verify chaotic behaviors through route of chaos; periodic motion (growing stage of confliction), chaotic motion (explosive stage or maximum stage of confliction), and periodic window (temporary coordinate stage of confliction) using phase portrait, bifurcation diagram and Lyapunov exponent.
ISSN:1562-2479
2199-3211
DOI:10.1007/s40815-022-01260-9