Linyun Huang

Behavior Analysis in Love Model of Romeo and Juliet with Time Delay

Abstract We say that human have an animal of emotion. There are various k ind in the emotion of human. One of among them, love has been studied in sociology and psychology a s a matter of great concern. In this paper, wepropose a novel love model with the delay time as response time for love. We also consider it in the Romeo and Juliet of love model to analyze their romantic behaviors. F irst we consider the Juliet only have a time delay, Romeo only have a time delay, and both Romeo and Juliet have a time delay. We represent their behaviors astime series and phase portrait, and we analyze their difference . Key Words : Periodic Motion, Quasi-Periodic Motion, Time-series, Phase P ortrait, Love Equation, Romeo, JulietReceived: Dec. 23, 2014Revised : Apr. 2, 2015Accepted: Apr. 7, 2015 † Corresponding author(ycbae@chonnam.ac.kr) 1. 서 론 우리가 살고 있는 세계는 복잡한 구조를 갖는 복잡계이다. 이러한 복잡한 구조 속에서 사람은 동물과는 다른 특성과 감정을 가지고 있다. 특히 사랑이라는 감정은 다른 동물에게는 존재하지 않는 독특한 감정영역의 하나이다. 따라서 사람은 사랑을 할 수 있고 또한 사랑을 받으면서 살아가는 존재이다. 사람들 사이에서 행해지는 사랑의 종류는 많이 있지만 그중에서도 남녀 간의 사랑은 사람의 감정 종류만큼 다양하고 많은 형태로 나타낸다. 더 큰 문제점은 이들 사랑을 모두 계량화하거나 수식화할 수 없다는 문제점이 존재한다. 이러한 상황에서 많은 연구자들에 의해 사랑에 대한 다양한 연구를 수행해 왔으며 앞으로도 많은 연구를 진행할 것으로 예상하고 있다. 지금까지 사랑에 대하여 생물학적, 생리학적, 철학적, 윤리적, 종교적인 연구가 있었지만 수학적으로 모델링하고 이들의 거동을 해석한 경우는 거의 없었다[1].사랑을 하나의 감정의 영역이므로 감정에 대한 수학적 표현에 대한 연구로서 중독 모델[2,3], 행복 모델[4-6], 사랑 모델[1,7-9]] 등이 연구되었다. 이들 연구들은 모두 시간 변화량에 대한 지각 등의 변화량을 중심으로 중독, 행복, 사랑에 대한 정의를 한 후 이 정의로부터 2차원의 미분 방정식을 유도하여 이들 거동으로부터 선형 또는 비선형적인 특성이 있음을 보인 것이 특징이다. 사람의 감정이외에 시스템에서 비선형적인 거동에 대한 연구[10-15]는 많이 진행해왔었으나 이는 사람이 아닌 시스템에 대한 것으로 사람의 감정과는 다른 영역의 해석이다. 사랑방정식에 대해서는 수학자들은 수학적 관점에서 사랑에 대한 정의를 해결하고자 하는 노력을 지속[1,5]하였으며 그 대표적으로 로미오와 줄리엣의 사랑을 들 수 있다[1,7-9]. 이들 로미

Chaotic Behavior in Model with a Gaussian Function as External Force

In this paper, we propose a novel dynamical love model of Romeo and Juliet, which has an external force with a fuzzy membership function. The external force used in the model has the characteristics of a Gaussian function. The chaotic behavior in the model is demonstrated using time series and phase portraits.

DSSS-Based Channel Access Technique DS-CDMA for Underwater Acoustic Transmission

This paper proposes a novel method for acoustically and wirelessly transmitting data underwater with a high transmission rate. The method uses the most promising physical layer and multiple access technique (i.e., the code division multiple channel access technique) to divide the channel into subchannels. Data is transmitted through these subchannels. The codes are PN (pseudo random) sequences. In the spread-spectrum technique, a signal such as electrical, electromagnetic, acoustic signal generated in a particular bandwidth is deliberately spread in the frequency domain, which results in a signal with a wider bandwidth. This paper reviews the possibility of application of the DS-CDMA (direct sequence-code division multiple access) technique in an underwater system using MATLAB. As the result of our review, we recognize that the DS-CDMA technique can be applied to underwater environments.

Analysis of Nonlinear Dynamics in Family Model including Parent-in-Law

Abstract Recently, it is emphasized importance of family. The new family organize including husband and wife are created by caused marriage, they organize new family including wife’s home and husband’s home. As a result, they may experience about conflict or peace between new family and previous family. The research of family mainly have been studied in the social science side. However, b ecause researchers of social science deals with linguistic emotion status, there is no mathematical modeling for family relationship. In this paper, one of the nonlinear research for social subject, we modify love model of Romeo and Juliet.Then we propose novel family relationship model for parent-in-law and daughter (or son)-in- law relation. We also confirm chaotic behavior or nonlinear behavior by time series and phase portrait.Key Words : Family, Nonlinear behavior, Chaotic phenomena, Phase portrait, Time seriesReceived: Dec. 24, 2015Revised : Jan. 4, 2016Accepted: Feb. 3, 2016

Measurement of DS-CDMA Propagation Distance in Underwater Acoustic Communication Considering Attenuation and Noise

It is very difficult to design an underwater communication system because of multipath, Doppler effects, noise, and attenuation. These factors lead to errors in the communication performance and maximum propagation distance. In this study, we calculate the distance that can be realized using the direct-sequence code division multiple access (DS-CDMA) technique with direct-sequence spread spectrum (DSSS) in an underwater communication system considering only the attenuation and noise. We also compare the estimated and calculated propagation distances obtained for several different scenarios.

Chaotic Dynamics of the Fractional-Love Model with an External Environment

Based on the fractional order of nonlinear system for love model with a periodic function as an external environment, we analyze the characteristics of the chaotic dynamic. We analyze the relationship between the chaotic dynamic of the fractional order love model with an external environment and the value of fractional order (α, β) when the parameters are fixed. Meanwhile, we also study the relationship between the chaotic dynamic of the fractional order love model with an external environment and the parameters (a, b, c, d) when the fractional order of the system is fixed. When the parameters of fractional order love model are fixed, the fractional order (α, β) of fractional order love model system exhibit segmented chaotic states with the different fractional orders of the system. When the fractional order (α = β) of the system is fixed, the system shows the periodic state and the chaotic state as the parameter is changing as a result.

Nonlinear Behavior in Romeo and Juliet’s Love Model Influenced by External Force with Fuzzy Membership Function

Recently, the study of chaotic behaviors in the social sciences includes the habit and the mind of human can be represented using models which include addiction, happiness, family relationship, and love. Within this field, various forms of love model have widely been studied. One of the most famous love models is the Romeo and Juliet model. To generate chaotic behaviors in the love model of Romeo and Juliet, it is necessary to apply an external force that is organized by a periodic function such as sine or cosine wave, which we assume as an ideal external force. However, because this ideal external force cannot possibly represent the real mind of a human, we need to find a reasonable function that allows us to closely describe the mind of human. In this paper, we propose a function that can describe the mind of human by using fuzzy membership function. To do this, we use Gaussian, sigmoid, and triangular fuzzy membership function as external forces. In order to get nonlinear behaviors by using computer simulation, we fix three parameters (a, c, and d) and vary parameter (b) for love model of Romeo and Juliet with the external forces of Gaussian, sigmoid, and triangular fuzzy membership function. Finally, we find that the external force that represents the nonlinear behaviors in love model of Romeo and Juliet through time series and phase portraits most excellent manner is the triangular fuzzy membership function.

Analysis of Chaotic Behavior in a Novel Extended Love Model Considering Positive and Negative External Environment

The aim of this study was to describe a novel extended dynamical love model with the external environments of the love story of Romeo and Juliet. We used the sinusoidal function as external environments as it could represent the positive and negative characteristics of humans. We considered positive and negative advice from a third person. First, we applied the same amount of positive and negative advice. Second, the amount of positive advice was greater than that of negative advice. Third, the amount of positive advice was smaller than that of negative advice in an external environment. To verify the chaotic phenomena in the proposed extended dynamic love affair with external environments, we used time series, phase portraits, power spectrum, Poincare map, bifurcation diagram, and the maximal Lyapunov exponent. With a variation of parameter “a”, we recognized that the novel extended dynamic love affairs with different three situations of external environments had chaotic behaviors. We showed 1, 2, 4 periodic motion, Rössler type attractor, and chaotic attractor when parameter “a” varied under the following conditions: the amount of positive advice = the amount of negative advice, the amount of positive advice > the amount of negative advice, and the amount of positive advice < the amount of negative advice.

Chaotic behavior in love affairs of fractional order with fuzzy membership function as an external force

This paper consider love affairs of fractional-order system with external force. To make chaotic behavior in the proposed fractional love model, we use fractional order differential equation that can be represented by Romeo and Juliets love affairs. We also apply triangular membership function as an external force, which can be closely represented human action or wording. Finally to confirm the chaotic behavior of proposed fractional-order love affairs with triangular membership function, which order is less than 3, we use time series and phase plane with changing parameter value.

Chaotic Dynamics of the Fractional-Love Model with an External Force

Based on the fractional order of nonlinear system for love model with a periodic function 10 as an external force, analyzed the characteristics of the chaotic dynamic in this study. The 11 relationship between the chaotic dynamic of the fractional-love model with the external force and 12 the fractional-order system was analyzed when the parameters are fixed. Further, we also studied 13 the relationship between the chaotic systemic dynamic and the parameters when the fractional14 order system is fixed. The results show that when the parameters are fixed, the fractional-order 15 system exhibited segmented chaotic states for the different fractional orders of the system. When 16 fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter 17 changes. 18