Interpretation:
To classify the fixed point at the origin of the system
Concept Introduction:
The Jacobian matrix at a general point
The eigenvalue
The solution of the quadratic equation is
The circle of maximum radius centered on the origin with all trajectories having radially outward component on it can be obtained by
The minimum radius circle centered on the origin with all trajectories having component directed radially inward on it can be found by putting
Nullclines are the curves in the phase portrait where
According to Poincare-Bendixson theorem, if a trapping region for a system does not contain any fixed point, then there must be at least one limit cycle within this trapping region.
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Nonlinear Dynamics and Chaos
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