Nonlinear ode: fixed points and linear stability

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An example of a nonlinear ode. How to compute fixed points and determine linear stability.

  1. Jeffrey Chasnov
  2. Differential Equation (Concepts/Theories)
  3. nonlinear
  4. fixed points
  5. linear stability
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Комментарии
Автор

Hi Sir hope you are having great time. I have a question regarding fixed point. In context of a function fixed point is defined as f(x) = x or standard notion is T(x)=x as given by Banach fixed point theorem. But in context of dynamical system when we use the word fixed point it seems that it doesn't relate to definition T(x) = x but rather we say that fixed point is where the derivative is zero. So my question is that does the word fixed point meaning differs in both contexts or is there any analogy.

advancedappliedandpuremath
Автор

The system is nonlinear but we are doing linear stability analysis. Why ?

onursimsek