Dynamical systems — equilibria and local stability
Analyse a smooth dynamical model through equilibrium solutions and a local linear approximation. Local eigenvalue behaviour does not by itself establish global stability or rule out nonlinear phenomena.
Rendering…
What this template contains
- Source
- 24 lines
Make it your own.
{
"nodes": [
{ "id": "ode", "type": "rounded", "label": "State equations and parameters", "x": 40, "y": 200, "width": 150, "height": 104, "fill": "#ede9fe", "stroke": "#6d28d9" },
{ "id": "domain", "type": "octagon", "label": "Admissible state domain", "x": 40, "y": 520, "width": 150, "height": 104, "fill": "#e0f2fe", "stroke": "#0369a1" },
{ "id": "eq", "type": "rounded", "label": "Solve stationary conditions", "x": 215, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
{ "id": "jac", "type": "rounded", "label": "Jacobian at each equilibrium", "x": 390, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
{ "id": "eig", "type": "card", "label": "Eigenvalues / local classification", "x": 565, "y": 200, "width": 150, "height": 104, "fill": "#ccfbf1", "stroke": "#0f766e" },
{ "id": "traj", "type": "card", "label": "Numerical trajectories", "x": 565, "y": 520, "width": 150, "height": 104, "fill": "#ccfbf1", "stroke": "#0f766e" },
{ "id": "bif", "type": "rounded", "label": "Parameter sensitivity", "x": 740, "y": 200, "width": 150, "height": 104, "fill": "#fef3c7", "stroke": "#b45309" },
{ "id": "global", "type": "rounded", "label": "Global / nonlinear limitations", "x": 740, "y": 520, "width": 150, "height": 104, "fill": "#f1f5f9", "stroke": "#475569" },
{ "id": "res", "type": "rounded", "label": "Stability statement with scope", "x": 915, "y": 200, "width": 150, "height": 104, "fill": "#fce7f3", "stroke": "#be185d" }
],
"edges": [
{ "id": "e0", "source": "ode", "target": "eq", "label": "set derivatives to zero" },
{ "id": "e1", "source": "domain", "target": "eq", "label": "filter admissible roots" },
{ "id": "e2", "source": "eq", "target": "jac", "label": "linearise" },
{ "id": "e3", "source": "jac", "target": "eig", "label": "classify" },
{ "id": "e4", "source": "ode", "target": "traj", "label": "explore initial conditions" },
{ "id": "e5", "source": "eig", "target": "bif", "label": "vary parameters" },
{ "id": "e6", "source": "traj", "target": "global", "label": "explore beyond local" },
{ "id": "e7", "source": "bif", "target": "res", "label": "local evidence" },
{ "id": "e8", "source": "global", "target": "res", "label": "qualify" }
]
}