On the numerical verification of the asymptotic expansion of duffing's equation

Monotonous property of non-oscillations of the damped Duffing’s equation

“…It has provided a useful paradigm for studies in nonlinear oscillations and chaotic dynamical systems, dating back to the development of approximate analytical methods based on perturbative ideas [1], and still continues, with the advent of fast numerical integration by computer, to be used as an archetypal illustration of chaos [2,[4][5][6][7]. Many profound results concerning various control, strange attractor, stability, chaotic behavior, periodic solutions and numerical simulations [1][2][3][4][5][6][7][8][9][10][11][12][13][14] et al have been established.…”

“…Note that under condition (14), Eq. (1) satisfies the Painlevé condition [18], so (15) can be also obtained through the Painlevé analysis [19].…”

Numerical Solution of Duffing Equation by Using an Improved Taylor Matrix Method

“…The Laplace decomposition method for numerical solution of Duffing equation has been 2 Journal of Applied Mathematics introduced by Yusufoglu [20] and Khuri [21]. On the other hand, Duffing differential equations have also been effectively dealt in many works [22][23][24][25][26][27][28][29].…”

A qualitative study of the damped duffing equation and applications

“…It has provided a useful paradigm for studying nonlinear oscillations and chaotic dynamical systems, dating back to the development of approximate analytical methods based on perturbative ideas [1], and continuing with the advent of fast numerical integration by computer, to be used as an archetypal illustration of chaos [2, [4][5][6][7]. Various methods for studying the damped Duffing equation and the forced Duffing equation in feedback control [8][9][10][11], strange attractor [12][13][14][15][16], stability [17][18][19], periodic solutions [20][21][22][23] and numerical simulations [24][25][26], etc., have been proposed and a vast number of profound results have been established. A phase plane analysis of the Duffing equation can be seen in [27] and more qualitative studies have been described in [28].…”