Figure 1
From: Flickering candle flames and their collective behavior
The figure from the left shows with a color-code the frequency of the limit-cycle oscillations in the \(a_u\), \(a_v\) parameters space, obtained from equations (3) using the parameters \(\varepsilon = {10}^{-3}\), \(c = 5.1\), \(\sigma _0=1\). In the dark-blue region there is no limit-cycle. For increasing the number of candles in the bundle (increasing the value of a) one moves in the direction of a line as indicated in the figure by the black arrow. The figure on the right side illustrates the variation of the frequency for the limit-cycle oscillations when the slope \(\varphi \) is constant and r is increasing. Here \(r=\sqrt{a_u^2+a_v^2}\) and \(\varphi =\arctan {(a_v/a_u)}\). Depending on the value of \(\varphi \) one might not get any oscillations (\(\varphi \ge 0.17\) rad for the indicated directions).
