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The object of the present paper is to find the fixed points and their stability by matrix method of the duffing equation (damped (δ ≠ 0) and unforced / undriven (γ = 0)) ?̈? + δ?̇? + (νx ± ρx) = γ cos(ωt), x = x(t), t = time period (1) using special case ν = 1 = ρ and taking the minus sign in (1), it becomes ?̈? + δ?̇? + (x − x) = 0 The duffing equation can be expressed in y2(t) and ?̇?2(t) shown by MATLAB program and their graphs.

Fixed points and Stability of Damped and Unforced Duffing Equation, Solution and Graphs for Displacement and Velocity of that Equation using Matlab