Global behavior in rational difference equations. Yevgeniy Kostrov

ISBN: 9781109288971

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NOOKstudy eTextbook

64 pages


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Global behavior in rational difference equations.  by  Yevgeniy Kostrov

Global behavior in rational difference equations. by Yevgeniy Kostrov
| NOOKstudy eTextbook | PDF, EPUB, FB2, DjVu, AUDIO, mp3, RTF | 64 pages | ISBN: 9781109288971 | 3.13 Mb

We investigate the global behavior of the solutions of several rational difference equations. In particular, we study the global stability, the periodic nature, and the boundedness character of their solutions. We investigate four equations in thisMoreWe investigate the global behavior of the solutions of several rational difference equations.

In particular, we study the global stability, the periodic nature, and the boundedness character of their solutions. We investigate four equations in this dissertation:-In the first manuscript we study the equation xn+1=a+bxn+g xn-1+dxn-2A+Bxn +Cxn-1+Dxn-2, n=0,1,... and we determine all special cases of this equation which possess an essentially unique period-two solution, and we pose several open problems and conjectures about their behavior.-In the second manuscript, we exhibit a range of parameters and a set of initial conditions where the rational difference equation xn+1=a+i=0 2kbixn-i A+j=0kB2j xn-2j, n=0,1,...

has unbounded solutions.-In the third manuscript, we give a detailed analysis of the forbidden set of the Riccati difference equation xn+1=an+b nxnAn+Bnx n,n=0,1,... where the coefficient sequences an infinityn=0, bninfinity n=0,A ninfinityn=0 ,Bn infinityn=0 are periodic sequences of real numbers with (not necessarily prime) period-2, and where the initial condition x0 ∈ R. The character of the solutions through the good points of the equation is also presented.-In the fourth manuscript, we give a detailed analysis of the character of solutions of the Riccati difference equation zn+1=a+bzn A+Bzn, n=0,1,...

where the coefficients alpha, beta, A, B are complex numbers, and where the initial condition z0 is a complex number.



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