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By Bryant D. E., Lindner C. C.

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1: The qualitative behavior of un = Ck n for different ranges of k, namely, −1 ≤ k ≤ 1. 3 Solve: xn+1 = xn 4 + yn , yn+1 = 3 x16n − yn 4 . Solution: xn xn xn+1 + yn ⇒ yn = xn+1 − ⇒ yn+1 = xn+2 − xn+1 = 4 4 4 Eliminating yn+1 from both the equations, we get, 4xn+2 − xn = 0 The required auxiliary equation is 4k 2 − 1 = 0 1 ⇒ k=± 2 The general solution is xn = c1 1 2 n + c2 −1 2 n 14 Mathematical Modeling: Models, Analysis and Applications where c1 and c2 are arbitrary constants. Similarly, it can be shown, yn = d1 1 2 n + d2 −1 2 n where d1 and d2 are arbitrary constants.

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2-perfectm-cycle systems can be equationally defined form=3, 5, and 7 only by Bryant D. E., Lindner C. C.


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