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nt) Consider the discrete-time dynamical system x1+1 = 4x,(1-x₂). If x₁ = ₁, X1+1 = Is x = an equilibrium for this system? Write the updating function rule as f(x) = 4x(1-x). Compute the derivative: f'(x) = Evaluate the derivative at the equilibrium: Is the equilibruim stable, unstable or neither?

nt) Consider the discrete-time dynamical system x1+1 = 4x,(1-x₂). If x₁ = ₁, X1+1 = Is x = an equilibrium for this system? Write the updating function rule as f(x) = 4x(1-x). Compute the derivative: f'(x) = Evaluate the derivative at the equilibrium: Is the equilibruim stable, unstable or neither?

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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nt) Consider the discrete-time dynamical system x+1 = 4x,(1-x₂). 3 If x₁ = ³, X₁+1 Is x₂ = an equilibrium for this system? X₁ 4 Write the updating function rule as f(x) = 4x(1-x). Compute the derivative: f'(x) = Evaluate the derivative at the equilibrium: Is the equilibruim stable, unstable or neither?
Transcribed Image Text:nt) Consider the discrete-time dynamical system x+1 = 4x,(1-x₂). 3 If x₁ = ³, X₁+1 Is x₂ = an equilibrium for this system? X₁ 4 Write the updating function rule as f(x) = 4x(1-x). Compute the derivative: f'(x) = Evaluate the derivative at the equilibrium: Is the equilibruim stable, unstable or neither?
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