Answered: Considering 2-by-2 nonlinear dynamical…

Considering 2-by-2 nonlinear dynamical system: x(n+1) = Xx(n)e¯ay(n); y(n+1) = cr(n)(1 — e−ay(n)) where X, a and c are positive model parameters:

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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Question

This question refers to a 2 by 2 nonlinear dynamical system. Please show all work for every part.

a) compute all steady state solutions and determine their stability

b) Confirm your analysis by plotting the long term solutions using specific values of λ, a and c.

This is an unsolved example from lecture notes.

Considering 2-by-2 nonlinear dynamical system:
x(n + 1) = x(n)e¯ay(n); y(n+1) = cx(n)(1 — e¯ªay(n))
, where X, a and c are positive model parameters:

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