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

RETRACTED: Applications of linear differential inclusion-based criterion to a nonlinear chaotic system: a critical review

“…Equation (22) is a ubiquitous model that arises in many physics and engineering contexts, such as the study of oscillations of a rigid pendulum undergoing moderately large amplitude motion, vibrations of a buckled beam and so on (Feng, 2006). There exist many sets of harmonic solutions in a chaotic system.…”

Characteristic Numbers of Matrix Lie Algebras

“…Remark 2 From Eqs. (11) and (18), we find that these two Lie algebras really are various. This fact is expressed by the explicit mathematical tools, i.e., the characteristic numbers γ 12 and γ 22 , which are used to distinguish the matrix Lie algebras for producing integrable couplings.…”

Residual Series Representation Algorithm for Solving Fuzzy Duffing Oscillator Equations

“…Duffing oscillator has been used to describe dwindling oscillatory motion with more complex capabilities than simple harmonic motion in the physical sense, to show the chaotic behaviors of nonlinear dynamic systems, and to display vibration jumps in the changing frequency phases of the periodically forced oscillator with nonlinear elasticity, along with many applications, including optimal control problems, robotics, electromagnetic pulses, and fuzzy modeling [6][7][8][9]. However, serious studies have been conducted to solve the Duffing equation, such as the study of a flexible pendulum motion that has a stiff spring that does not follow Hooke's law, and the study of non-harmonic external perturbations [10][11][12]. In most cases where the entries may be precise (crisp) or imprecise (fuzzy), the variables, parameters, or conditions were considered in crisp terms.…”