Amplitudedependent

Amplitude-dependent, often written as amplitude-dependent or amplitude dependent, describes a property of a system where its response varies with the amplitude of the input or oscillation. This is a hallmark of nonlinear behavior, in contrast to linear systems whose response remains proportional to input regardless of size.

Common manifestations include an amplitude-dependent frequency, where the natural or resonant frequency shifts as oscillation amplitude grows, a phenomenon seen in nonlinear oscillators such as Duffing-type systems. It can also appear as amplitude-dependent damping or loss, in which dissipation changes with amplitude, and as amplitude-dependent saturation or gain in electronic, optical, or mechanical devices. The result is often distortion, generation of harmonics, or changes in effective impedance as the input increases.

A typical mathematical description involves nonlinear terms in the governing equations. For example, a Duffing oscillator is modeled by x'' + δ x' + α x + β x^3 = F cos(ωt), where the cubic term β x^3 introduces an amplitude-dependent shift in resonance. More generally, nonlinear responses can be expressed as outputs that depend on higher powers of input amplitude, such that y = f(x, A) with f nonlinear in A.

Amplitude-dependent effects appear across fields, including electrical circuits with saturated amplifiers, mechanical and MEMS resonators, and nonlinear optical media where field intensity alters refractive or absorptive properties. They can complicate calibration and control but are also exploited in applications like nonlinear signal processing and sensitive measurements.

See also: nonlinear dynamics, Duffing oscillator, Kerr effect, nonlinear impedance.