Duffing equation

Duffing equation

Fractals and chaos

Published in A. W. Jayawardena, Environmental and Hydrological Systems Modelling, 2013

Although the Duffing equation (Duffing, 1918) was first published for studying classic oscillators in electronics, it has later found applications in biology, particularly in the study of modelling the brain. The equation displays catastrophic jumps of amplitude and phase for gradual changes of the forcing frequency term. It is also considered as the simplest non-linear forced damped oscillator. In a mechanical system, the equation models a spring pendulum whose spring constant (stiffness) does not strictly obey Hooke’s law. The most general form of the Duffing equation, which is a second-order non-linear ordinary differential equation, is () d2xdt2+αdxdt+f(x)=e(t)

Unique solutions, stability and travelling waves for some generalized fractional differential problems

View Article

Journal Information

Published in Applied Mathematics in Science and Engineering, 2023

Mahdi Rakah, Yazid Gouari, Rabha W. Ibrahim, Zoubir Dahmani, Hasan Kahtan

The Duffing phenomenon is named after Georg Duffing, and refers to the nonlinear behaviour of a mechanical system, such as a spring-mass system, that experiences both damping and a periodic forcing. The nonlinearity results in the occurrence of a variety of dynamic behaviours, including limit cycles and chaos, which are not present in linear systems. The Duffing equation is widely used as a model to study nonlinear vibrations and chaos in various fields, including mechanical engineering, physics, and control systems. The Duffing equation is a nonlinear, second-order ordinary differential equation that describes the dynamics of a system subjected to a periodic driving force and a nonlinear restoring force (see [1–5]).

Explore chapters and articles related to this topic

Fractals and chaos

Unique solutions, stability and travelling waves for some generalized fractional differential problems