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- W1969192011 abstract "The major task of qualitative analysis of systems of ordinary differential equations is to recognize the global pattern of solution curves in the phase space. In this paper, I present a flow grammar, a grammatical specification of all possible patterns of solution curves one may see in the phase space. I describe a flow pattern, a semi-symbolic representation of the patterns of solution patterns in the phase space and show how an important class of flow patterns can be specified by the flow grammar. I then show that the flow grammar presented in this paper can generate any flow pattern resulting from any structurally stable flow on a plane. I also describe several properties of the flow grammar related to the enumeration of patterns. In particular, I estimate the upper limit of the number of applications of rewriting rules needed to derive a given flow pattern. Finally, I describe how the flow grammar is used in qualitative analysis to plan, monitor and interpret the result of numerical computation." @default.
- W1969192011 created "2016-06-24" @default.
- W1969192011 creator A5007474538 @default.
- W1969192011 date "1997-03-01" @default.
- W1969192011 modified "2023-09-27" @default.
- W1969192011 title "Grammatical description of behaviors of ordinary differential equations in two-dimensional phase space" @default.
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- W1969192011 doi "https://doi.org/10.1016/s0004-3702(96)00055-0" @default.
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