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Suppose that the population x, of bacteria satisfies the discrete time dynamical system X1 where r is a parameter, and 0

Suppose that the population x, of bacteria satisfies the discrete time dynamical system X1 where r is a parameter, and 0

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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X1+1= Suppose that the population x, of bacteria satisfies the discrete time dynamical system Xt where r is a parameter, and 0 <r < 1. r+ (x₂)² If x = 0, what is X₁+1? Is x* = 0 an equilibrium? If x₁ = √√/1-7, what is X₁+1 ? Is x* = √√/1-r an equilibrium? Write the updating function rule as f(x) = Compute the derivative: f'(x) = x* = √1-r is stable? C What condition on guarantees that the equilibrium
Transcribed Image Text:X1+1= Suppose that the population x, of bacteria satisfies the discrete time dynamical system Xt where r is a parameter, and 0 <r < 1. r+ (x₂)² If x = 0, what is X₁+1? Is x* = 0 an equilibrium? If x₁ = √√/1-7, what is X₁+1 ? Is x* = √√/1-r an equilibrium? Write the updating function rule as f(x) = Compute the derivative: f'(x) = x* = √1-r is stable? C What condition on guarantees that the equilibrium
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