dynamic_1d_solve
Analyze 1D autonomous dynamical systems by computing equilibria, stability, phase portraits, and time series for custom or standard models.
Instructions
Analyze the 1D autonomous system x' = f(x): equilibria, stability, phase portrait and time series.
Args: func_str: f(x) used when model is 'custom'. model: 'custom' | 'malthus' (rx) | 'verhulst' (mux*(1-x/K)) | 'newton' (-k*(x-Ta)). params: parameter values, e.g. {'r': 1.5} or {'mu': 1.0, 'K': 2.0}. x_min, x_max: state window. t_max: final time of the time series. n_phase: resolution of the phase analysis. n_time: number of time steps. initial_conditions: starting states, e.g. [0.1, 1.0]. control_enabled: add a constant control term -h (verhulst/custom only).
Returns: Dict with equilibria, their stability, the phase portrait data and time solutions.
Input Schema
| Name | Required | Description | Default |
|---|---|---|---|
| model | No | custom | |
| t_max | No | ||
| x_max | No | ||
| x_min | No | ||
| n_time | No | ||
| params | No | ||
| n_phase | No | ||
| func_str | No | x | |
| control_enabled | No | ||
| initial_conditions | No |