Mathematical Modelling and Chaotic Behavior Analysis of Cyber Addiction

Abstract

Addiction can be largely divided into two categories. One is called medium addiction in which medium itself causes an addiction. Another is called cause addiction that brings addiction through combination of sensitive self and latent personal action. The medium addiction involves addiction phenomena directly caused by illegal drugs, alcohol and various other chemicals. The cause addiction is dependent on personal sensitivities as a sensitive problem of personal and includes cyber addictions such as shopping, work, game, internet, TV, and gambling. In this paper we propose two-dimensional addiction model that are equivalent to using an R-L-C series circuit of Electrical circuit and a Spring-Damper-mass of mechanical system. We also organize a Duffing equation that is added a nonlinear term in the proposed two-dimensional addiction model. We represent periodic motion and chaotic motion as time series and phase portrait according to parameter's variation. We confirm that among parameters chaotic motion had addicted state and periodic motion caused by change in control coefficient had pre-addiction state.

Chaotic Behavior in Model with a Gaussian Function as External Force

“…In particular, studies on chaotic behaviors in the social sciences, including those related to habits and the human mind, such as addiction [1][2][3][4], happiness [5][6][7][8], and love models [8][9][10][11][12][13], involve an overlap of the fields of mathematics, biology, psychology, and social science.…”

“…Bae and his colleagues [1][2][3][4] proposed a mathematical model for addictions to digital leisure, internet, tobacco, and physical exercise. Further, they also verified the presence of nonlinear behaviors or chaotic phenomena by using time series and phase portraits.…”

Chaotic Behavior in a Dynamic Love Model with Different External Forces

“…Recently, some researchers have been interested in models for addiction [8][9][10][11], happiness [12][13][14][15], and love [15][16][17][18][19][20], which involve an overlap of mathematics, biology, psychology, and social science.…”

“…Bae [8][9][10] and Bae and Kim [11] proposed a mathematical model for addictions to digital leisure, internet use, tobacco use, and physical exercise. He also confirmed the presence of nonlinear or chaotic phenomena, using time series and phase portraits.…”

Mathematical Modelling and Behavior Analysis of Addiction of Physical Exercise

“…또한 배영철은 사이버 중독에서의 2차원 모델을 제시 [10]하였으며, 행복 모델에서의 동기화 현상에 대한 연구 [11], 행복 모델에서의 비선형거동 [12], 사랑 모델에서의 거동 해석 [13] …”