Abstract
This paper presents a comprehensive stability analysis of the dynamics of the damped cubic-quintic Duffing oscillator. We employ the derivative expansion method to investigate the slightly damped cubic-quintic Duffing oscillator obtaining a uniformly valid solution. We obtain a uniformly valid solution of the un-damped cubic-quintic Duffing oscillator as a special case of our solution. A phase plane analysis of the damped cubic-quintic Duffing oscillator is undertaken showing some chaotic dynamics which sends a signal that the oscillator may be useful as model for prediction of earth- quake occurrence.
Highlights
Most real life problems are nonlinear in nature
This paper presents a comprehensive stability analysis of the dynamics of the damped cubic-quintic Duffing oscillator
It is very important to note that in the phase plots obtained for 1, the phase lines tend to converge to the equilibrium points while for 1, the phase lines diverge from the equilibrium points to infinity. This development is in harmony with the solution we obtained in (32) for the damped and forced cubic-quintic Duffing oscillator where, setting 0, we found out that the exponential function depicting the damping grows larger and tends to infinity
Summary
Most real life problems are nonlinear in nature. The Duffing oscillator is one of such important nonlinear system. System (2) below describes the motion of the cubic Duffing oscillator which can be used to model conservative double well oscillators which can occur in magnetoelastic mechanical systems [1]. The cubic Duffing equation can as well be used to model the nonlinear spring-mass system [3,4], as well as the motion of a classical particle in a double well potential [5]. The Duffing oscillator can be described by the following equation of motion: U dH dy. The damped and forced cubic-quintic Duffing oscillator with random noise obtained by setting N 2 in (1) is given by the equation.
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