dynamic_1d_bifurcation
Perform bifurcation analysis of one-dimensional dynamical systems by sweeping a parameter and tracking equilibria to reveal critical transitions and stability changes.
Instructions
Bifurcation analysis of x' = f(x; bif_param): equilibria vs parameter sweep.
Args: func_str: f(x) used when model is 'custom'. model: 'custom' | 'malthus' | 'verhulst' | 'newton'. params: values of the other model parameters, e.g. {'K': 2.0}. bif_param: name of the bifurcation parameter swept between bif_min and bif_max. bif_min, bif_max, bif_steps: parameter sweep range/resolution. x_min, x_max, n_phase: state window for finding equilibria. phase_params: optional explicit parameter values for phase slices. control_enabled: add a constant control term -h (verhulst/custom only).
Returns: Dict with the equilibria-vs-parameter table, exact symbolic analysis and phase slices.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| model | No | custom | |
| x_max | No | ||
| x_min | No | ||
| params | No | ||
| bif_max | No | ||
| bif_min | No | ||
| n_phase | No | ||
| func_str | No | x | |
| bif_param | No | r | |
| bif_steps | No | ||
| phase_params | No | ||
| control_enabled | No |