From 19eff12131365c7c7285a323acc12377f0eb6457 Mon Sep 17 00:00:00 2001
From: KangWon LEE <kangwon@gmail.com>
Date: Wed, 22 May 2024 17:53:31 +0900
Subject: [PATCH] 50 / 60 : add descriptions of the simulations

help from Gemini
---
 50_ode/60_Duffing_Oscillator.ipynb | 36 ++++++++++++++++++++++++++++++
 1 file changed, 36 insertions(+)

diff --git a/50_ode/60_Duffing_Oscillator.ipynb b/50_ode/60_Duffing_Oscillator.ipynb
index ac557868..d52af5ed 100644
--- a/50_ode/60_Duffing_Oscillator.ipynb
+++ b/50_ode/60_Duffing_Oscillator.ipynb
@@ -206,6 +206,15 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "e98fb788-3ade-431c-a128-eb80178293df",
+   "metadata": {},
+   "source": [
+    "* Weak forcing near the natural frequency.\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -224,6 +233,15 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "ec5c37b1-cca9-4466-aaaf-a1043fe2ec6e",
+   "metadata": {},
+   "source": [
+    "* Stronger forcing, potentially leading to nonlinear effects.\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -240,6 +258,15 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "5baf7fc6-28f4-4b0f-82ee-0d3ab34f49f6",
+   "metadata": {},
+   "source": [
+    "* Exploring different resonance regions.\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
@@ -288,6 +315,15 @@
     "\n"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "id": "3fc29623-aa3c-4d7a-b327-a559a421dec6",
+   "metadata": {},
+   "source": [
+    "* Sweeping omega to look for period-doubling bifurcations and chaos.\n",
+    "\n"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,