A population is governed by the nonlinear equationx = x² - 3x3 +2.Show that there is an equilibrium state at x = 1 and by considering a small pertur-bation determine whether it is a stable or unstable state. Find any other equilibriumstates and determine their stability.

To analyze the given nonlinear equationx˙=x4−3x3+2,we start by finding the equilibrium states, which…

Answered: A population is governed by the…

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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A population is governed by the nonlinear equation x = x² - 3x3 +2. Show that there is an equilibrium state at x = 1 and by considering a small pertur- bation determine whether it is a stable or unstable state. Find any other equilibrium states and determine their stability.