All Questions
Tagged with complex-systems oscillators
4 questions
2
votes
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Linearized equations
What is $V_{\alpha\beta}$?
And what is a symmetric, positive definite potential energy matrix?
And why is there a linearized equation like this?
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Is there a relation between large-scale oscillations and small-scale oscillations?
From Neural oscillation - Wikipedia:
Oscillatory activity in the brain is widely observed at different levels of organization and is thought to play a key role in processing neural information.
In ...
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2
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How to justify this small angle approximation $\dot{\theta}^2=0$?
Suppose the equation of motion for some oscillating system takes the following form:
$$\ddot{\theta}+\dot{\theta}^2\sin\theta+k^2\theta\cos\theta=0$$
Applying small angle approximation to $\theta$ ...
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Is there a relation between phase plane and complex plane?
The only occurrence I see complex numbers used in dynamical systems is to analyse the eigenvalue $\lambda$ of the linearised approximation to determine the characteristics of equilibrium points. ...
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