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...v criterion is applicable only to autonomous (that is, [[time invariant]]) systems. The sub-class of Lur'e systems studied by [[Vasile M Popov|Popov]] is described by: ...

{{distinguish|text=[[Gardner's relation]], a nonlinear equation in rock physics}} The '''Gardner equation''' is an [[integrable]] [[nonlinear partial differential equation]] introduced by the mathematician [[Clifford ...

...Nyquist stability criterion]] for [[LTI system|linear time-invariant (LTI) systems]]. Consider a linear system subject to non-linear feedback, i.e., a nonlinear element <math>\varphi(v, t)</math> is present in the feedback loop. Assume ...

...eriodic output of a stable, [[Causal system|causal]], [[time invariant]] [[nonlinear system]] to a [[Sine wave|sinusoidal]] input signal: ...the application of HOSIDFs to (nonlinear) controller design for nonlinear systems is shown to yield significant advantages over conventional time domain base ...

...Korteweg–de Vries (KdV) equation''' is an [[Integrable system|integrable]] nonlinear [[partial differential equation]]:{{sfn | Polyanin | Zaitsev | 2003}} ...| first=Andrei D. | last2=Zaitsev | first2=Valentin F. | title=Handbook of Nonlinear Partial Differential Equations | publisher=Chapman and Hall/CRC | publicati ...

...ov–Wilson (DSW) equations''' are an [[integrable system]] of two coupled [[nonlinear]] [[partial differential equation]]s proposed by [[Vladimir Drinfeld]] and [[Category:Nonlinear partial differential equations]] ...

...plates, diffraction gratings, and many other common optical components and systems. * The [[superposition principle]] is valid for linear-optical systems. For example, if a mirror transforms light input A into output B, and input ...

...bn=0-7803-0210-9|s2cid=28613314}}</ref> TSM is [[Robust control|robust]] [[Nonlinear control|non-linear control]] approach. ...this convergence may only be guaranteed within infinite time. In TSM, a [[nonlinear]] term is introduced in the sliding surface design so that the manifold is ...

{{Short description|Formulas to determine the energy balance of a nonlinear wave}} ...wave that has multiple frequencies. They have since been found to describe systems in [[non-linear optics]],<ref> ...

...] (either [[linear equation system|linear]] or [[nonlinear equation system|nonlinear]]) is called '''consistent''' if there is at least one set of values for th The nonlinear system ...

..., or '''VSS''', is a [[Classification of discontinuities|discontinuous]] [[nonlinear system]] of the form ...ntinuity of these systems, they behave like different continuous nonlinear systems in different regions of their [[state space (controls)|state space]]. At th ...

...for determining local [[bifurcation theory|bifurcations]] in a system. All systems exhibiting a certain type of bifurcation are locally (around the equilibriu ...ath> u = x -1, \mu = r + 1 </math>.<ref name="strogatz">Strogatz, Steven. "Nonlinear Dynamics and Chaos". Westview Press, 2001. p. 52.</ref> ...

...ef>{{Cite journal |last=van Kampen |first=E. R. |date=1941 |title=Notes on Systems of Ordinary Differential Equations |url=https://www.jstor.org/stable/237153 == Linear systems of differential equations == ...

...23b2065-479d-4ee5-92de-85ddf4ce6ec2}}</ref> MSPC can be used to quantify [[nonlinear]] phase coupling between a set of base frequencies and their [[harmonic]]/[ ...th>\langle \cdot \rangle</math> represents the average over [[Realization (systems)|realizations]]. ...

...tem]]s this is independent of amplitude. The mixing of modes in non-linear systems is termed [[resonant interaction]]. ...s with the [[natural frequency|eigen-frequency]] of the system (linear and nonlinear resonance correspondingly). Vibrational modes can interact in a [[resonant ...

In [[control theory]], [[dynamical systems theory|dynamical systems]] are in '''strict-feedback form''' when they can be expressed as Here, ''strict feedback'' refers to the fact that the [[nonlinear system|nonlinear]] functions <math>f_i</math> and <math>g_i</math> in the <math>\dot{z}_i</m ...

...e=Lyapunov–Malkin Theorem and Stabilization of the Unicycle Rider |journal=Systems and Control Letters |volume=45 |issue=4 |pages=293–302 |doi=10.1016/S0167-6 ...hbb{R}^m\times \mathbb{R}^n \to \mathbb{R}^n</math> represent higher-order nonlinear terms. If all [[eigenvalue]]s of the matrix <math>A</math> have negative re ...

...as wave shape distortion and the emergence of solitary waves in dispersive systems.<ref>{{Cite journal |last=Biswas |first=Anjan |date=2009 |title=Solitary wa [[Category:Nonlinear partial differential equations]] ...

[[nonlinear control]] system with one scalar nonlinearity, which belongs to the sector ...e conjecture]]. This conjecture was proven false but led to the (valid) [[Nonlinear control#Absolute stability problem|sufficient criteria on absolute stabilit ...

...isbn=978-981-02-4694-5 }}</ref> was proven false but led to the (valid) [[Nonlinear control#Absolute stability problem|sufficient criteria on absolute stabilit ...large (i.e. unique stationary point is global [[attractor]]) if all linear systems with f(e)=ke, k ∈(k1,k2) are asymptotically stable.'' ...