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

한국전자통신학회 (Korea Institute of Electronic Communication Science)
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Van der Pol 발진기에서의 미분방정식과 Fractional 미분방정식의 거동 비교 해석

Comparison Analysis of Behavior between Differential Equation and Fractional Differential Equation in the Van der Pol Equation

  • 배영철 (전남대학교 전기.전자통신.컴퓨터공학부)
  • Bae, Young-Chul (Division of Electrical.Electronics Communication and Computer Engineering, Chonnam National University)
  • 투고 : 2015.12.23
  • 심사 : 2016.01.24
  • 발행 : 2016.01.30
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초록

300년 전에 발표한 fractional calculus의 개념인 fractional 미분 방정식을 제어공학, 수학, 물리학 등에 적용하고자 하는 노력이 지속되고 있다. 본 논문에서는 Van der Pol 방정식으로 표현되는 동적 방정식을 정수 차수와 실수 차수를 가진 fractional 차수로 표현하고 실수 차수의 값을 변화시켜 가면서 시계열 데이터와 위상공간으로 정수 차수와 실수 차수의 비교를 수행한다.

Three hundred years ago, the fractional differential equation that is one of concept of fractional calculus released. Now, many researchers continue to try best effort applying into the control engineering, mathematics and physics. In this paper, the dynamics equation which is represented by Van der Pol, represent integer order and fractional order that having real order. Then this paper performs the comparisons between integer and real order as time series and phase portrait according to variation of parameter value for real order.

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