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Understanding the notion and intuition behind the definition of $\Gamma_x$ (orbit through $x$)?

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#ordinary-differential-equations #dynamical-systems
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Why do real positive eigenvalues result in an unstable system? What about eigenvalues between 0 and 1? or 1?

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#linear-algebra #eigenvalues-eigenvectors #dynamical-systems #stability-theory
85
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Suppose $\dot{x}=Ax$, where $A \in \mathbb{R}^{2\times2}$. Determine $A$ from the initial and final states

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#ordinary-differential-equations #systems-of-equations #dynamical-systems #system-identification
9k
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Why are they called "first integrals"?

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#ordinary-differential-equations #dynamical-systems
40
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Phase portrait of $u_{xx} + u(1-u)(u-0.5)$?

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#ordinary-differential-equations #partial-differential-equations #dynamical-systems
1.2k
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Finding the stable, unstable, center manifolds of a nonlinear system

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#ordinary-differential-equations #systems-of-equations #dynamical-systems #nonlinear-system
203
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Global stability question for system with a unique locally-asymptotically-stable steady state

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#ordinary-differential-equations #dynamical-systems #mathematical-modeling #stability-in-odes
182
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Optimization problems in non-linear and linear differential equations

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#ordinary-differential-equations #optimization #dynamical-systems
238
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Nonlinear map having conserved quantity

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#dynamical-systems #nonlinear-system #nonlinear-dynamics
121
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In frictionless rigid-body collision dynamics, what happens when a ball falls into a crevice where two planes intersect?

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#dynamical-systems #physics #classical-mechanics
62
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What are some methods for finding global stability for this 3D system?

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#ordinary-differential-equations #dynamical-systems #mathematical-modeling #stability-in-odes
52
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Feedforward control extra dynamics needed?

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#dynamical-systems #control-theory
130
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Filippov dynamical system

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#ordinary-differential-equations #dynamical-systems
406
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Proving that a second order system is not exponentially stable

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#ordinary-differential-equations #dynamical-systems #stability-theory #lyapunov-functions
497
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Discrete maps: Stability of periodic orbits

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#dynamical-systems #nonlinear-system

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