Abstract
Consider a system of two first-order coupled ODEs of the general structure
where P and Q are known functions of the dependent variables X and Y, and the independent variable has been taken to be the time t. In other model equations, the independent variable could be a spatial coordinate, e.g., the Cartesian coordinate x. For compactness, the dot notation of (1.1) will often be used in our text discussion for time derivatives, one dot denoting d/dt, two dots standing for d2/dt2, and so on. Superscripted primes on the dependent variable indicate a spatial derivative, e.g., Y′ ≡ dY/dx, Y″ ≡ d2Y/dx2, etc.
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© 2007 Springer Science+Business Media, LLC
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(2007). Phase-Plane Portraits. In: Computer Algebra Recipes. Springer, New York, NY. https://doi.org/10.1007/978-0-387-49333-6_2
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DOI: https://doi.org/10.1007/978-0-387-49333-6_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-25768-6
Online ISBN: 978-0-387-49333-6
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