Chaos ¤×ÍÍÐäÃáÅзÓäÁàÃÒ¶Ö§µéͧ¾Ù´¶Ö§¤Ó æ ¹Õé
                    㹪ÕÇÔµ»ÃШÓÇѹàÇÅÒàÃÒ¾Ù´¶Ö§ÊÔè§ËÃ×͵èÒ§ æ ·ÕèàÃÒäÁèÊÒÁÒö·Õè¨Ð¤Ò´à´Ò¼ÅÀÒÂ˹éÒä´éäÁèÇèÒ¨Ò¡¡ÒÃÇÑ´ËÃ×Í¡ÒÃ
Êѧࡵ áÅоٴÃÇÁàÍÒÊÔ觷ÕèàÃÒàËç¹ÇèÒà»ç¹Ãкº·ÕèäÁèÁÕÃÐàºÕºËÃ×ÍÁͧäÁèàË繤ÇÒÁà¡ÕèÂÇ¢éͧÃÐËÇèÒ§¡Ñ¹ªÑ´à¨¹ ÇèÒ Chaos
                    áµè¤ÇÒÁà»ç¹¨Ãԧ㹷ҧÇÔ·ÂÒÈÒʵÃì àÇÅÒàÃÒ¾Ù´¶Ö§ Chaos àÃÒ¨ÐËÁÒ¶֧"Deterministic Chaos"à·èÒ¹Ñ鹫Ö觨ӡѴ     ãËéÃкº·ÕèàÃÒ¾Ù´¶Ö§ÇèÒ Ãкº¢Í§àÃÒà»ç¹Ãкº·Õè¢Ö鹡Ѻ¤èÒàÃÔèÁµé¹ â´ÂÊÀÒÇлѨ¨ØºÑ¹¢Ö鹡ѺÊÀÒÇСè͹˹éÒ¹Õéà·èÒ¹Ñé¹â´ÂàÃÒäÁèÃÇÁ àÍÒÃкº·ÕèÁÕ¡ÒÃà¡Ô´¢Öé¹áººÊØèÁ·ÕèäÁèä´é¢Ö鹡Ѻ¤èÒàÃÔèÁµé¹ àªè¹ ¡ÒÃâ¹àËÃÕ­·Õè¤èÒ·Õèä´é㹤ÃÑé§ÅèÒÊØ´¨ÐäÁèà¡ÕèÂÇ¢éͧ¡Ñº¤èÒ¤ÃÑ駡è͹

             áÅéǵ¡Å§ Chaos ¤×ÍÍÐäà ?
                    à»ç¹¤Ó¶ÒÁ·ÕèÂÒ¡¨ÐËҤӵͺ·Õè´Õä´é áÅСçÁÕ¼Ùé¹ÔÂÒÁä»ËÅÒÂæ ẺµÒÁÅѡɳФÇÒÁÃÙéáÅФÇÒÁà¢éÒ㨢ͧµ¹ áµè¡çà»ç¹ä»ã¹·ÔÈ·Ò§à´ÕÂǡѹ ¨Ðà»ç¹¡ÒôաÇèÒËÒ¡¨Ð·Ó¤ÇÒÁà¢éÒ㨴éǹÔÂÒÁ·Õèà»ç¹ÀÒÉÒÍѧ¡ÄÉ ã¹·Ò§¤³ÔµÈÒʵÃì¡çÍÒ¨
¹ÔÂÒÁ¤ÃèÒÇ æ ä´éà»ç¹ “effectively unpredictable long time behavior arising in a deterministic dynamical system because
of sensitivity to initial conditions.”
                    Êèǹ㹷ҧÇÔ·ÂÒÈÒʵÃì¡ÒÂÀÒ¾áÅÐÇÔÈÇ¡ÃÃÁÈÒʵÃì¹Ñé¹¹ÔÂÒÁãËéÊÍ´¤Åéͧ¡Ñº¢éÍ¡Ó˹´ä´é´Ñ§¹Õé

1. The underlying dynamics is deterministic;
2. No external noise has been introduced;
3. The seeming erratic behavior of individual trajectories  depend sensitively on small changes of initial conditions;
4. In contrast to a single trajectory, some global characteristics, obtained by averaging over many trajectories or over long time;
5. And, when a parameter is tuned, the erratic state is reached via a sequence of events, usually including the appearance of one or more subharmonics;

                  Nonlinear science ?
                      ÍÒ¨à»ç¹¡ÒÃà¢éÒ㨼ԴËÒ¡¾Ù´ÃÇÁÇèÒ»ÃÒ¡¯¡ÒóìµèÒ§ æ à»ç¹ chaos ·Ñé§ËÁ´ áµè¶éÒËÒ¡¨Ð¾Ù´ãËé¶Ù¡µéͧ ¤×Í »ÃÒ¡¯¡ÒóìµèÒ§ æ ·Ø¡ÍÂèÒ§à»ç¹ nonlinear à¾ÃÒÐäÁèÁÕ model ¨ÃÔ§ã´ã¹¸ÃÃÁªÒµÔ·Õèà»ç¹ linear à¾Õ§áµè linear modelÊÒÁÒö ãËé¡ÒûÃÐÁÒ³·Õè´Õä´é㹺ҧ real model 㹺ҧà§×è͹ä¢à·èÒ¹Ñé¹ áµèàÁ×èÍ¢¹Ò´¢Í§ÃкºãË­è¢Öé¹ËÃ×;ԨÒóҷÑé§Ãкº àÃÒ¡ç¨Ð
¾º ¤ÇÒÁ¨ÃÔ§ÇèÒà»ç¹ nonlinear system «Öè§ÊÒÁÒöÁÕËÅÒ æ ÊÔ觷Õèá»Å¡ËÃ×;ÔàÈÉ¡ÇèÒ·ÕèàÃÒ¤Ò´¤Ô´ áÅÐ nonlinearity ¡çÂѧáÊ´§ effect ·Õèà¡ÕèÂÇ¢éͧÅÖ¡«Ö駡Ѻ dynamical system ´Ñ§¹Ñé¹ nonlinear system ·ÕèàÃÒ¾ºÍÒ¨¨Ðà»ç¹Ãкº·Õèà»ç¹ chaos ËÃ×Í äÁèà»ç¹
chaos ¡çä´é ¢Öé¹ÍÂÙè¡Ñº nonlinearity ¢Í§ÃкºÇèÒà»ç¹ dynamical system Ẻã´
                       ÊÓËÃѺ nonlinear science ¶×Íà»ç¹ÊÒ¢ÒÇÔªÒ·ÕèÁÒ classified à»ç¹ÇÔªÒÂèÍÂäÁèä´é à¾ÃÒÐàÃÒÂѧäÁèÊÒÁÒö¨Óṡ
Ãкº nonlinear ÇèÒÁÕÊèǹã´à»ç¹Êèǹ·Õè«Ñº«é͹à»ç¹ chaos, Êèǹ¹Õéà»ç¹Êèǹ·ÕèÁÕÃÐàºÕº´Õ ÏÅÏ ãËéªÑ´à¨¹ä´é ´Ñ§¹Ñé¹àÁ×è;ٴ¶Ö§
nonlinear system áÅéÇàÃÒËÁÒ¶֧·Ñé§Ãкº nonlinear science ¨Ö§»ÃСͺ´éÇ·ء æ ÊÒ¢Òã¹ÇÔ·ÂÒÈÒʵÃì ÃÇÁ件֧·Ò§¡ÒÃ
á¾·Âì, àÈÃÉ°ÈÒʵÃì áÅÐÇÔÈÇ¡ÃÃÁÈÒʵÃì  ÊÔè§Ë¹Ö觷Õè¹èÒµ×è¹àµé¹¤×ÍÊÒÁÒö·ÓãËé·Ø¡ÊÒ¢Ò·ÕèᵡµèÒ§¡Ñ¹¾Ù´ã¹ÀÒÉÒà´ÕÂǡѹ