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Aug 22, 2014 at 11:12 comment added Joonas Ilmavirta @XingdongZuo, can you be more specific what you want? I cannot give a rigorous proof for a vague claim. I understood from your claim that you want the limit $\lim_{t\to\infty}\rho(t)$ not to exist. I extended my answer a bit to show this and more.
Aug 22, 2014 at 11:11 history edited Joonas Ilmavirta CC BY-SA 3.0
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Aug 22, 2014 at 9:07 comment added Xingdong Zuo Thanks for the answer. Yes, we can show that the 'general' derivative is away from zero. Well, but we'd like to know that the solution will fluctuate forever(up and down behaviors, intuitively in graphs), because there can be case that the derivative is nonzero, but the solution is already in an equilibrium (not fluctuate any more).
Aug 22, 2014 at 8:59 history answered Joonas Ilmavirta CC BY-SA 3.0