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Results tagged with differential-equations
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user 77927
Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.
0
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Accepted
How to prove that a non-linear differential equation has a solution
Before attempting anything complicated (such as the theory of Differential Algebraic Equations), I would try to put it in a standard first-order ODE form. By the chain rule:
$$w'(y-f(y))(1-f'(y))=g(y) …
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3
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1
answer
98
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Examples of systems with stable equilibria at the boundary of the phase space
Hopfield networks are gradient dynamical systems, used (among other things) to solve combinatorial optimization problems, because stable equilibria are at vertices of the hypercube $[-1,1]^n$. They ha …
- 274
3
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Nonlinear ODE system: stability
Another approach would be to expand in series form around some equilibrium point, and observe whether the lower order terms resemble some "known" behaviour, which is known as a normal form on the cent …
- 274
2
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Accepted
Quadratic stability of linear time varying system
Sure: take the scalar ODE $\dot x=-x$, with $A=-1$, which is exponentially stable and the state transition matrix is $\Phi(t)=e^{-t}$ (i.e. $x(t)=\Phi(t) x_0$). Assume $Q=e^{2t}$, which is not bounded …
- 274
2
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Fit a system of linear ODEs from several experiments
(This is more of a comment but not enough reputation to do)
It seems a case for system identification (e.g. http://es.mathworks.com/products/sysid/) but I do not get the dependence on $p$, does it st …
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