Question

Duffing's equation is interesting in that it exhibits bifurcation, or dependence of stability properties and number of equilibrium points on a parameter. For the undamped Duffing equation given by

y¨​+αy+y³ = 0
Represent the system in state-space form.

Answer 1

The Duffing equation can be represented in state-space form by defining two state variables and writing first-order differential equations. The state-space representation of the Duffing equation is x₁' = x₂ and x₂' = -αx₁ - x₁³.

Step-by-step explanation:

The Duffing equation, given by y¨ + αy + y³ = 0, can be represented in state-space form. State-space representation is a mathematical model used to describe the behavior of a system over time.

To convert the Duffing equation into state-space form, we define two state variables, x₁ and x₂, and write two first-order differential equations: x₁ = y and x₂ = y'. The state-space representation of the Duffing equation is:

x₁' = x₂

x₂' = -αx₁ - x₁³