The Journal of the Korea institute of electronic communication sciences (한국전자통신학회논문지)

Korea Institute of Electronic Communication Science (한국전자통신학회)
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Analysis of Chaotic Behavior in Fractional Duffing Equation

Fractional Duffing 방정식에서의 카오스 거동 해석

  • Bae, Young-Chul (Division of Electrical.Electronics Communication and Computer Engineering, Chonnam National University)
  • 배영철 (전남대학교 전기.전자통신.컴퓨터공학부)
  • Received : 2015.11.10
  • Accepted : 2015.12.24
  • Published : 2015.12.31
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Abstract

Recently many effort appears applying the concept of fractional calculus that can be represented by fractional differential equation in the control engineering, physics and mathematics. This paper describes the fractional order with real order for Duffing equation which can be represented by integer order. This paper also confirms the existence of chaotic behaviors by using time series and phase portrait with varying the parameter of real order.

최근에 fractional calculus의 개념을 적용하여 fractional 미분 방정식으로 표현되는 기법이 제어공학, 수학, 물리학 등에 적용하고자 하는 노력이 나타나고 있다. 본 논문에서는 Duffing 방정식으로 표현되는 동적 방정식을 정수 차수가 아닌 fractional 차수로 표현하고 이 fractional 실수 차수에서 차수의 크기에 따라 카오스 거동이 존재함을 실수 차수의 값을 변화시켜가면서 시계열 데이터와 위상공간으로 확인하고자 한다.

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