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Dynamics of second order rational difference equations : with open problems and conjectures / M.R.S. Kulenovioc, G. Ladas.

M. R. S Kulenovioc, (Mustafa R. S.)

Boca Raton, FL : Chapman & Hall/CRC, ©2002.

Online access

  • Title:
    Dynamics of second order rational difference equations : with open problems and conjectures / M.R.S. Kulenovioc, G. Ladas.
  • Author: M. R. S Kulenovioc, (Mustafa R. S.)
  • Contributor: G. E Ladas
  • Subjects: Difference equations -- Numerical solutions; Équations aux différences -- Solutions numériques; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Difference equations -- Numerical solutions; Electronic books;
    Dewey: 515/.625
  • Rights: Terms governing use: Copyright.
    Access restrictions: NON_PRINT_LEGAL_DEPOSIT
  • Publication Details: Boca Raton, FL : Chapman & Hall/CRC, ©2002.
  • Language: English
  • Description: Contents: INTRODUCTION AND CLASSIFICATION OF EQUATION TYPES
    PRELIMINARY RESULTS
    Definitions of Stability and Linearized Stability Analysis
    The Stable Manifold Theorem in the Plane
    Global Asymptotic Stability of the Zero Equilibrium
    Global Attractivity of the Positive Equilibrium
    Limiting Solutions
    The Riccati Equation
    Semicycle Analysis
    LOCAL STABILITY, SEMICYCLES, PERIODICITY,

    Contents: AND INVARIANT INTERVALS
    Equilibrium Points
    Stability of the Zero Equilibrium
    Local Stability of the Positive Equilibrium
    When is Every Solution Periodic with the same Period?
    Existence of Prime Period Two Solutions
    Local Asymptotic Stability of a Two Cycle
    Convergence to Period Two Solutions when C=0
    Invariant Intervals
    Open Problems and Conjectures
    (1, 1)-TYPE EQUATIONS
    Introduction
    The Case a=g=A=B=0: xn+1= b xn/C xn-1
    The Case a=b=A=C=0: xn+1=g xn-1/B xn
    Open Problems and Conjectures
    (1, 2)-TYPE EQUATIONS
    Introduction
    The Case b=g=C=0: xn+1= a /(A+ B xn)
    The Case b=g=A=0: xn+1= a /(B xn+ C xn-1)
    The Case a=g=B=0: xn+1= b xn/(A + C xn-1)
    The Case a=g=A=0: xn+1= b xn/(B xn+ C xn-1)
    The Case a=b=C=0: xn+1= g xn-1/(A+ B xn)
    The Case a=b=A=0: xn+1= g xn-1/(B xn+ C xn-1)
    Open Problems and Conjectures
    (2, 1)-TYPE EQUATIONS
    Introduction
    The Case g=A=B=0: xn+1=(a + b xn)/(C xn-1)
    The Case g=A=C=0: xn+1=(a + b

    Contents: xn)/B xn
    Open Problems and Conjectures
    (2, 2)-TYPE EQUATIONS(2, 2)- Type Equations
    Introduction
    The Case g=C=0: xn+1=(a + b xn)/(A+ B xn)
    The Case g=B=0: xn+1=(a + b xn)/(A + C xn-1)
    The Case g=A=0: xn+1=(a + b xn)/(B xn+ C xn-1)
    The Case b=C=0: xn+1=(a + g xn-1)/(A+ B xn)
    The Case b=A=0: xn+1=(a + g xn-1)/(B xn+ C xn-1)
    The Case a=C=0: xn+1=(b xn+ g xn-1)/(A+ B xn)
    The Case a=B=0: xn+1=(b xn+ g xn-1)/(A + C xn-1)
    The Case a=A=0: xn+1=(b xn+ g xn-1)/(B xn+ C xn-1)
    Open Problems and Conjectures
    (2, 3)-TYPE EQUATIONS
    Introduction
    The Case g=0: xn+1=(a + b xn)/(A+ B xn+ C xn-1)
    The Case b=0: xn+1=(a + g xn-1)/(A+ B xn+ C xn-1)
    The Case a=0: xn+1=(b xn+ g xn-1)/(A+ B xn+ C xn-1)
    Open Problems and Conjectures
    (3, 2)-TYPE EQUATIONS
    Introduction
    The Case C=0: xn+1=(a + b xn+ g xn-1)/(A+ B xn )
    The Case B=0: xn+1=(a + b xn+ g xn-1)/(A+ C xn-1)
    The Case A=0: xn+1=(a + b xn+ g xn-1)/(B xn+ C xn-1)
    Open Problems and

    Contents: Conjectures
    THE (3, 3)-TYPE EQUATION The (3, 3)- Type Equation: xn+1=(a + b xn+ g xn-1 )/(A+ B xn+ C xn-1)
    Linearized Stability Analysis
    Invariant Intervals
    Convergence Results
    Open Problems and Conjectures
    APPENDIX: Global Attractivity for Higher Order Equations
    BIBLIOGRAPHY

  • Identifier: ISBN 142003538X (electronic bk.); ISBN 9781420035384 (electronic bk.); ISBN 9781584882756; ISBN 1584882751; ISBN (cloth); BNB GBB7C6837; System number: 018428264
  • Notes: Bibliography note: Includes bibliographical references and index.
  • Physical Description: 1 online resource (xi, 218 pages) : illustrations.
  • Shelfmark(s): General Reference Collection DRT ELD.DS.160495
  • UIN: BLL01018428264

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