Dynamics of second order rational difference equations : with open problems and conjectures /: with open problems and conjectures. (©2002)

• Record Type: Book
• Further Information: Note: M.R.S. Kulenovioc, G. Ladas.
• Other Names: Kulenovioc, M. R. S (Mustafa R. S.); Ladas, G. E
• 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, 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 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 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
• Publisher Details: Boca Raton, FL : Chapman & Hall/CRC
• Publication Date: 2002
• Copyright Date: 2002
• Extent: 1 online resource (xi, 218 pages), illustrations
• Subjects: 515/.625; Difference equations -- Numerical solutions; Équations aux différences -- Solutions numériques; MATHEMATICS -- Calculus; MATHEMATICS -- Mathematical Analysis; Difference equations -- Numerical solutions; Electronic books
• Languages: English
• ISBNs: 9781420035384; 9781584882756; 1584882751
• Related ISBNs: 142003538X; 1584882751
• Notes: Note: Includes bibliographical references and index.; Note: Print version record.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.