Systematics in bifurcations of exponential growth equations with a non-linear feedback

Walter Seifritz

Energy, 1995, vol. 20, issue 3, 169-172

Abstract: Bifurcation phenomena may be examined in terms of the class of non-linear differential equations of the first kind in the form ẋ(t) = αnβx(t) − {x(t)}n+1, where α and β are constants and n is an integer. A transformation of variables is applied taking into account the initial values x(0) = x0. The solutions are presented in the form of dimensionless variables and in polar coordinates to visualize limit cycles. The well known logistic and pitchfork equations (n = 1 and 2, respectively) are special cases, as is also the equation for explosive population growth (n = 1, α and β imaginary).

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:eee:energy:v:20:y:1995:i:3:p:169-172

DOI: 10.1016/0360-5442(94)00075-E

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