> For the complete documentation index, see [llms.txt](https://yinqi-h.gitbook.io/ml-models/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://yinqi-h.gitbook.io/ml-models/models/differential-equations/ordinary-differential-equations/language-ordinary-differential-equations-ode.md).

# Language Ordinary Differential Equations (ODE)

| Model                                                             | Growth Level | Time  | Growth Rate           | Carrying Capacity | Un-utilized Opportunity | Delay | Forgetting |
| ----------------------------------------------------------------- | ------------ | ----- | --------------------- | ----------------- | ----------------------- | ----- | ---------- |
| Exponential Growth Without Feedback Delay                         | $$L\_t$$     | $$T$$ | $$r = L\_t+\_1-L\_t$$ |                   |                         |       |            |
| Logistic Growth Without Feedback Delay                            | $$L\_t$$     | $$T$$ |                       | $$K$$             | $$U=K-L$$               |       |            |
| Restricted Growth Without Feedback Delay                          | $$L\_t$$     |       |                       |                   |                         |       |            |
| Feedback Delay and Approximative, Oscillatory, and Chaotic Growth | $$L\_t$$     |       |                       |                   |                         |       |            |
| Learning and Forgetting Under Limited Resources                   | $$L\_t$$     |       |                       |                   |                         |       |            |
| Inferring Intermediate Growth Points in the Difference Equation   |              |       |                       |                   |                         |       |            |
| A Measure for Growth Efficiency                                   |              |       |                       |                   |                         |       |            |