Please provide a stability analysis to determine if this steady state is stable or unstable. Use a process that satisfies these 3 inequalties: Determinant(Jacobian) > -1 + Trace(Jacobian) Det(J) > -1 - Tr(J)

Please provide a stability analysis to determine if this steady state is stable or unstable. Use a process that satisfies these 3 inequalties: Determinant(Jacobian) > -1 + Trace(Jacobian) Det(J) > -1 - Tr(J)

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. The steady state solution is y*=ln(λ)/a and x*= cλ-c

Please provide a stability analysis to determine if this steady state is stable or unstable.

Use a process that satisfies these 3 inequalties:

Determinant(Jacobian) > -1 + Trace(Jacobian)

Det(J) > -1 - Tr(J)

Det(J) < 1

This an unsolved example from lecture, please help. Class is mathematical modeling.

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:

Expert Solution

Step 1: Find jacobian matrix and fixed points.

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