Interpretation:
To find fixed points, draw nullclines,
Concept Introduction:
Fixed point of a differential equation is a point where
Nullclines are the curves where either
Vector fields in this aspect represent the direction of flow and whether flow is going away from fixed point or coming towards it.
Phase portraits represent the trajectories of the system with respect to the parameters and give qualitative idea about evolution of the system, its fixed points, whether they will attract or repel the flow etc.
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Nonlinear Dynamics and Chaos
- Use the direction field to sketch the graphs of the solutions that satisfy the given initial conditions. (a) y(0) = 1(b) y(0) = 2(c) y(0) = –1arrow_forwardFind the equilibrium solutions of dy/dx=2y(y-2), and based on the direction field, determine the behavior of y as x->infinity, including any dependency on the value y(0).arrow_forwardFind the equilibrium solution of the following equation, make a sketch of the direction field, for t ≥ 0, and determine whether the equilibrium solution is stable. The direction field needs to indicate only whether solutions are increasing or decreasing on either side of the equilibrium solution.arrow_forward
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