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Normal form of Transcritial bifurcation

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#dynamical-systems
73
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$\int_0^{\infty} e^{A^*t} e^{At} dt$ is well-defined when $\mu(A) < 0$

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#real-analysis #ordinary-differential-equations #dynamical-systems
182
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Equivalent ODE forward integration

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#ordinary-differential-equations #numerical-methods #dynamical-systems #vector-fields
353
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Converting Second Order IVP to an Autonomous System With the Parameters Treated as Unknowns

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#calculus #ordinary-differential-equations #dynamical-systems
61
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Direction which trajectories tend to a node sigularity

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#ordinary-differential-equations #dynamical-systems
282
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An introduction to Lagrangian and Hamiltonian mechanics well suited for people familiar with convex optimization

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#reference-request #convex-optimization #dynamical-systems #control-theory #classical-mechanics
2.1k
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How to plot a phase space

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#ordinary-differential-equations #multivariable-calculus #dynamical-systems
44
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Transformation maps between different Poincare sections

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#dynamical-systems
93
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What is the general definition of thickness of a strange attractor?

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#dynamical-systems #complex-dynamics
73
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Critical points of autonomous ODEs

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#real-analysis #ordinary-differential-equations #dynamical-systems
172
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Explanation on the Proof of $W(t)=W(t_0)\exp\left(\int_{t_0}^{t} \text{tr}(\underline{A}(s)) \ ds\right)$

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#proof-verification #proof-explanation #dynamical-systems
83
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Periodic solutions with period converging to $0$ converge to equilibrium

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#real-analysis #ordinary-differential-equations #dynamical-systems
53
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If $X(t)$ is a $2\times 2$ fundamental matrix, prove that $W(t)=W(t_0)\exp\left(\int_{t_0}^{t} \text{tr}(\underline{A}(s)) \ ds\right).$

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#calculus #dynamical-systems
221
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Does heteroclinic intersections of the stable and unstable manifolds of different fixed points imply chaotic behavior?

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#dynamical-systems #chaos-theory #fixed-points #nonlinear-dynamics
210
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Linearized equation of motion

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#dynamical-systems

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