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(교)2 + a (7) + aT = T (피)3 + (a-1)교 =0 F{(7) + (a – 1)} = 0 e equilibrium points are 0 and t/1- a. ||

(교)2 + a (7) + aT = T (피)3 + (a-1)교 =0 F{(7) + (a – 1)} = 0 e equilibrium points are 0 and t/1- a. ||

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.9: Properties Of Determinants
Problem 46E
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Explain the determine purple and inf is here and Why did we choose this equilibrium point?

Proposition [22] Assume that p,q € R. Then \p| + |q] < 1 is a sufficient condition for the asymptotic stability of the difference equation Хn+1 — рап — qxn-1 — 0, п 3 0, 1,... . Lemma 1. The equilibrium points of the difference equation (2) are 0 and ±/1- a Proof. (x) + a (7)° + ax = X (7) + (a – 1) = 0 7{(T) + (a – 1)} = 0 This means that the equilibrium points are 0 and ±/1 – a.
Transcribed Image Text:Proposition [22] Assume that p,q € R. Then \p| + |q] < 1 is a sufficient condition for the asymptotic stability of the difference equation Хn+1 — рап — qxn-1 — 0, п 3 0, 1,... . Lemma 1. The equilibrium points of the difference equation (2) are 0 and ±/1- a Proof. (x) + a (7)° + ax = X (7) + (a – 1) = 0 7{(T) + (a – 1)} = 0 This means that the equilibrium points are 0 and ±/1 – a.
Motivated by the above studies, we study the dynamics of following higher order difference equation Xn+1 A + B (2) п-т where A, B are positive real numbers and the initial conditions are positive numbers. Additionally, we investigate the boundedness, periodicity, oscillation behaviours, global asymptotically stability and rate of convergence of related higher order difference equations.
Transcribed Image Text:Motivated by the above studies, we study the dynamics of following higher order difference equation Xn+1 A + B (2) п-т where A, B are positive real numbers and the initial conditions are positive numbers. Additionally, we investigate the boundedness, periodicity, oscillation behaviours, global asymptotically stability and rate of convergence of related higher order difference equations.
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