Linearizing ordinary differential equations

thavamaran
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Hi guys, I am trying to linearize a coupled non-linear ode. I used partial derivative, and then jacobian matrix, i have seen paper using state-space model of jacobian matrix. I can't get a proper reference on this state-space model.

Attached is the non-linear ode, the partial derivative of the non-linear ode and the state-space model of jacobian matrix.

Can someone enhance or explain how they got the state-space model as the transformation, is it a fix formulation. Sorry for asking this way cause I can't find any books or reference referring or explaining this. Please help me! thanks!
 
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Thread 'Direction Fields and Isoclines'

Thread 'Direction Fields and Isoclines'

I sketched the isoclines for $$ m=-1,0,1,2 $$. Since both $$ \frac{dy}{dx} $$ and $$ D_{y} \frac{dy}{dx} $$ are continuous on the square region R defined by $$ -4\leq x \leq 4, -4 \leq y \leq 4 $$ the existence and uniqueness theorem guarantees that if we pick a point in the interior that lies on an isocline there will be a unique differentiable function (solution) passing through that point. I understand that a solution exists but I unsure how to actually sketch it. For example, consider a...
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