词条 | Kaplan–Yorke map |
释义 |
The Kaplan–Yorke map is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior. The Kaplan–Yorke map takes a point (xn, yn ) in the plane and maps it to a new point given by where mod is the modulo operator with real arguments. The map depends on only the one constant α. Calculation methodDue to roundoff error, successive applications of the modulo operator will yield zero after some ten or twenty iterations when implemented as a floating point operation on a computer. It is better to implement the following equivalent algorithm: where the and are computational integers. It is also best to choose to be a large prime number in order to get many different values of . Another way to avoid having the modulo operator yield zero after a short number of iterations is Xn+1 = 2Xn (mod 0.99995) Yn+1 = αYn + cos(4πXn) which, will still eventually return zero but takes many more iterations. References
1 : Chaotic maps |
随便看 |
|
开放百科全书收录14589846条英语、德语、日语等多语种百科知识,基本涵盖了大多数领域的百科知识,是一部内容自由、开放的电子版国际百科全书。