DYNAMICAL BEHAVIOR AND SOLUTION OF NONLINEAR DIFFERENCE EQUATION VIA FIBONACCI SEQUENCE
E. M. Elsayed, Faris Alzahrani, Ibrahim Abbas, Nehal Alotaibi
Abstract
In this paper, we study the behavior of the difference equation $x_{n+1}=ax_{n}+\dfrac{bx_{n}x_{n-1}}{cx_{n-1}+dx_{n-2}},~n=0,1,\ldots,$ where the initial conditions $x_{-2},\ x_{-1},\ x_{0}$ are arbitrary positive real numbers and $a,b,c,d$ are positive constants. Also, we give the solution of some special cases of this equation.
Topics & Concepts
Fibonacci numberMathematicsSequence (biology)Nonlinear systemMathematical analysisCombinatoricsPhysicsChemistryQuantum mechanicsBiochemistryMathematical and Theoretical Epidemiology and Ecology ModelsNonlinear Differential Equations AnalysisFractional Differential Equations Solutions