Related papers: Reciprocity of nonlinear systems
We report on the demonstration of an effective, nonlinearity-induced non-reciprocal behavior in a single non-magnetic multi-mode Taiji resonator. Non-reciprocity is achieved by a combination of an intensity-dependent refractive index and of…
Based on the Maxwell-Beatty reciprocity theorem, static non-reciprocity has been realized by using nonlinearity, but this non-reciprocity has strict restrictions on input amplitude and structure size (number of units). Here, we propose a…
There are many notions of symmetry for state space models. They play a role in understanding when systems are time reversible, provide a system theoretic interpretation of thermodynamics, and have applications in certain stabilization and…
Reciprocal relations correlate fairly accurately a great variety of experimental results. Nevertheless, the concepts of statistical fluctuations, and microscopic reversibility - the bases of the accepted proof of the relations by Onsager -…
We report an experimental and theoretical investigation of a system whose dynamics is dominated by an intricate interplay between three key concepts of modern physics: topology, nonlinearity, and spontaneous symmetry breaking. The…
We present two linked theorems on passivity: the passive behavior theorem, parts 1 and 2. Part 1 provides necessary and sufficient conditions for a general linear system, described by a set of high order differential equations, to be…
We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…
Non-reciprocal interactions, where the influence of agent $i$ on $j$ differs from that of $j$ on $i$, are fundamental in active and living matter. Yet, most models implement such asymmetry phenomenologically. Here we show that…
The concept of passivity is central to analyze circuits as interconnections of passive components. We illustrate that when used differentially, the same concept leads to an interconnection theory for electrical circuits that switch and…
Parity-time (PT) symmetry is of great interest. The reciprocal and unidirectional features are intriguing besides the PT symmetry phase transition. Recently, the reciprocal transmission, unidirectional reflectionless and invisibility are…
Nonreciprocity, a hallmark of nonequilibrium systems, can generate dynamics not possible near thermodynamic equilibrium, including oscillatory and rotating patterns. The onset of temporal oscillations is often evident in linearized…
This paper deals with the analysis of nonlinear circuits that interconnect passive elements (capacitors, inductors, and resistors) with nonlinear resistors exhibiting a range of $\it{negative}$ resistance. Such active elements are necessary…
Simple nonlinear dynamical systems with multiple stable stationary states are often taken as models for switchlike biological systems. This paper considers the interaction of multiple such simple multistable systems when they are embedded…
Interactions between active particles may be non-reciprocal, breaking action-reaction symmetry and leading to novel physics not observed in equilibrium systems. The non-reciprocalCahn-Hilliard (NRCH) model is a phenomenological model that…
Stability and control of a non-linear system represent an important system configuration that frequently arises in practical engineering. Stability covers a vast range of systems that do not obey the superposition principle and applies to…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Understanding how biological homochirality emerged remains a challenge for the researchers interested in the origin of life. During the last decades, stable non-racemic steady states of nonequilibrium chemical systems have been discussed as…
Non-reciprocal interactions are a generic feature of non-equilibrium systems. We define a non-reciprocal generalization of the kinetic Ising model in one spatial dimension. We solve the model exactly using two different approaches for…
Investigations of scattering in presence of non-linearity which have just begun require the confinement of both the potential, $V(x)$, and the non-linearity, $\gamma f(|\psi|)$. There could be two options for the confinement. One is the…
We study the breaking of reciprocity in non-Hermitian coupled photonic waveguides by the simultaneous action of the nonlinear effect of saturable absorption, and the presence of exceptional points. The nonlinear response of such a system is…