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- W4382516396 abstract "Example 2.1 (power series emerge). Recall the linear dynamics of Example 1.1: a linear transform separated the emergent dynamics from ignorable transients. But most scientific dynamics are nonlinear. So now consider the toy nonlinear dynamics ofwhere, as always, overdots denote d/dt. The numerical solutions plotted in Figure 2.1 demonstrate that all solutions quickly collapse onto a curve in the u1u2-plane. Thus the long-time emergent dynamics lies on this curve. But over long times do the solutions stay within the picture? Or do they “explode” to infinity? Linearly, as in Example 1.1, the long-time dynamics is u1 = u2 . In the case when u1 = u2 precisely, then the quadratic reactions remove as much as they generate, so simple arguments, such as linear transforms or averaging, cannot predict the effective long-time influence of the nonlinear terms." @default.
- W4382516396 created "2023-06-30" @default.
- W4382516396 date "2014-01-01" @default.
- W4382516396 modified "2023-09-24" @default.
- W4382516396 title "Chapter 2: Power series solve ordinary differential equations" @default.
- W4382516396 doi "https://doi.org/10.1137/1.9781611973563.ch2" @default.
- W4382516396 hasPublicationYear "2014" @default.
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