# Lotka-Volterra Systems3. 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). Showthat the trajectory (a(t),g() corresponds to a periodic solution if and only if it isclosed curve in the ry-plane parametrized by time.

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pls explain to me step by step. thanks help_outlineImage TranscriptioncloseLotka-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. fullscreen
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Step 1

To establish the (given) necessary and sufficient conditions for the periodicity of solutions of the given system

Step 2

Point to note in the problem: the fact that x(t) and y(t) are solutions of a system (of differential equations) is not relevant to the periodicity to be discussed.

Step 3

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