A Geometric Approach to Dynamical Systems in ℝ N

Reimund Rautmann

A chapter in Applied Nonlinear Analysis, 2002, pp 443-456 from Springer

Abstract: Abstract In 2-dimensional dynamical systems defined by some differential equation $$ \dot x = f(x) $$ , global existence and asymptotics of the solutions follow from a geometric condition concerning the characteristics, on which one component of the vector function f is vanishing. By extending this geometric condition to n dimensions we find 2 classes of differential equations which have global solutions for all positive times. Additional monotonicity of the characteristics implies the existence of a unique stationary point which is asymptotically stable and globally attractive.

Keywords: Dynamical systems; characteristics condition; flow invariant rectangles; global existence; attractors (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-0-306-47096-7_30

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DOI: 10.1007/0-306-47096-9_30

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