Dynamics of Second Order Rational Difference Equations
11%
off

Dynamics of Second Order Rational Difference Equations : With Open Problems and Conjectures

By (author)  , By (author) 

Free delivery worldwide

Available. Dispatched from the UK in 3 business days
When will my order arrive?

Description

This self-contained monograph provides systematic, instructive analysis of second-order rational difference equations. After classifying the various types of these equations and introducing some preliminary results, the authors systematically investigate each equation for semicycles, invariant intervals, boundedness, periodicity, and global stability. Of paramount importance in their own right, the results presented also offer prototypes towards the development of the basic theory of the global behavior of solutions of nonlinear difference equations of order greater than one. The techniques and results in this monograph are also extremely useful in analyzing the equations in the mathematical models of various biological systems and other applications. Each chapter contains a section of open problems and conjectures that will stimulate further research interest in working towards a complete understanding of the dynamics of the equation and its functional generalizations-many of them ideal for research projects or Ph.D. theses. Clear, simple, and direct exposition combined with thoughtful uniformity in the presentation make Dynamics of Second Order Rational Difference Equations valuable as an advanced undergraduate or a graduate-level text, a reference for researchers, and as a supplement to every textbook on difference equations at all levels of instruction.show more

Product details

  • Hardback | 232 pages
  • 163.1 x 242.8 x 18.5mm | 552.39g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • New.
  • 3 black & white tables
  • 1584882751
  • 9781584882756
  • 2,413,701

Table of 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 BIBLIOGRAPHYshow more