Global aspects of Riccati differential and difference equations
Chapter
Abstract
Riccati differential equations are among the simplest non-linear differential equations and, clearly, then initial value problems can be solved locally. But, in contrast to linear systems of differential equations, their solutions may show the phenomenon of finite escape time . This generally means that after a finite time interval the solution ceases to exist. One of the simplest examples showing these features is the scalar Riccati differential equation with the real solution .
$$
y' = 1 + y^2 ,
$$
$$
y(x) = \tan (x + c),c \in \mathbb{R}
$$
with the real solutions
Keywords
Periodic Solution Phase Portrait Riccati Equation Representation Formula Algebraic Riccati Equation
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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© Springer Basel AG 2003