Nonlinear Systems: Global Theory

  • Lawrence Perko
Part of the Texts in Applied Mathematics book series (TAM, volume 7)


In Chapter 2 we saw that any nonlinear system
$$ \dot{x}=f(x) $$
with fC1(E) and E an open subset of R n , has a unique solution Φ t (x0), passing through a point x0E at time t=0 which is defined for all tI(x0), the maximal interval of existence of the solution. Furthermore, the flow Φ t of the system satisfies (i) Φ0(x)=x and (ii) Φ t +s(x)=Φ t (Φ s (x)) for all x ∈ E and the function Φ(t, x)=Φ t (x) defines a C1-map Φ:Ω → E where Ω={(t, x) ∈R × E | tI(x)}.


Periodic Orbit Phase Portrait Stable Limit Cycle Global Theory Quadratic System 
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Copyright information

© Springer-Verlag New York, Inc. 1996

Authors and Affiliations

  • Lawrence Perko
    • 1
  1. 1.Department of MathematicsNorthern Arizona UniversityFlagstaffUSA

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