Lotka-Volterra Systems 3. A solution (t,r(t). y(t)) of the system (t)f((t),yt) y(t) = g(x(t), y(t)) is called periodic if for some T and all t > 0 x(t +T) = x(t) and y(t + T) = y(t). Show that the trajectory (a(t),g() corresponds to a periodic solution if and only if it is closed curve in the ry-plane parametrized by time.

Lotka-Volterra Systems 3. A solution (t,r(t). y(t)) of the system (t)f((t),yt) y(t) = g(x(t), y(t)) is called periodic if for some T and all t > 0 x(t +T) = x(t) and y(t + T) = y(t). Show that the trajectory (a(t),g() corresponds to a periodic solution if and only if it is closed curve in the ry-plane parametrized by time.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Lotka-Volterra Systems
3. A solution (t,r(t). y(t)) of the system
(t)f((t),yt)
y(t) = g(x(t), y(t))
is called periodic if for some T and all t > 0 x(t +T) = x(t) and y(t + T) = y(t). Show
that the trajectory (a(t),g() corresponds to a periodic solution if and only if it is
closed curve in the ry-plane parametrized by time.

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