Fuzzy Control for Chaotic Confliction Model
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Fuzzy Control for Chaotic Confliction Model Jin Hee Yoon1
•
Gwi-Man Bak2 • Youngchul Bae3
Received: 13 January 2020 / Revised: 1 March 2020 / Accepted: 7 March 2020 Ó Taiwan Fuzzy Systems Association 2020
Abstract Nowadays, the research for chaotic dynamics in the social science has been interested by many researchers. This paper proposes a fuzzy controlling method for dynamic confliction model between certain group A and group B based upon love affairs model. In order to control the confliction between group A and group B, we apply control input with the symmetry triangular fuzzy numbers, which are special fuzzy numbers into each group A and group B. We show the result of fuzzy control for chaotic confliction model by using time series and phase portrait while we apply control input with specific time domain. Keywords Chaotic control Chaotic confliction model Coordination Fuzzy numbers Time series Phase portrait Lyapunov exponent Bifurcation diagram
& Youngchul Bae [email protected] Jin Hee Yoon [email protected] Gwi-Man Bak [email protected] 1
Sch. Mathematics and Statistics, Sejong University, Seoul, South Korea
2
Dep. Electrical Eng, Chonnam National Univ, Yeosu, South Korea
3
Div. Electrical, Electronic Communication and Computer Eng, Chonnam National Univ, Yeosu, South Korea
1 Introduction Over the past four decades, many scholars and researchers have been interested in chaotic dynamics in various fields including mathematics, physics, chemistry, engineering, and social sciences. Among these academic areas, the research of chaotic dynamics in the social sciences, including the social phenomena, habit, and the mind of human being, can be represented as addiction [1–4], happiness [5–8], family relationship [9, 10], international arms race and outbreak of war [11, 12] and love model [13–32]. The mathematical addiction models regarding digital leisure addiction, cyber space addiction including mobile device and computer games, smart phone addiction, habit addiction including tobacco and drug use, and physical exercise have been proposed by Bae et al. [1–4]. Also mathematical human being emotion model including happiness model [5–8] and love affairs model, such as the Romeo and Juliet model [13–24], the Laura and Petrarch model [25, 26], the Adam and Eve model [27], and other including fractional order love model [28–32], has been also proposed by many researchers. Recently, the social relationship model regarding family relationship [9, 10], international arms race, and outbreak of war [11, 12] also has been studied by many researchers. Nowadays, many conflictions take place in the human life among human, society, and the nation. The conflict phenomena mainly focus on the subject in economic science, social science, psychological science, and so on. These science deals with phenomena of confliction and its controlling method in the viewpoint of finding solution of confliction. There are several research for confliction model including one-shot conflicting game [33–35], a dynamic model i
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