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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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Chapter 6 Solutions
Nonlinear Dynamics and Chaos
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- Q4*) (make sure you first understand question P5) Discuss the extremisation of the integral I = = √(2(y + 2) ³y' + (x − 7)) c You may find point (iv) in § 3.5 relevant. dx.arrow_forwardQ6*) Describe the plane paths of light in the two-dimensional media in which the light velocities are given respectively by (a) c = a/y, (b) c = a/√y, where a > 0, y > 0.arrow_forwardlim 1 x→0x3 3 So²² 6 tln(1+t) t4 +4 .dt 2arrow_forward
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