Related papers: Reciprocity of nonlinear systems
Many interesting phenomena in nature are described by stochastic processes with irreversible dynamics. To model these phenomena, we focus on a master equation or a Fokker-Planck equation with rates which violate detailed balance. When the…
Diverse equilibrium systems with heterogeneous interactions lie at the edge of stability. Such marginally stable states are dynamically selected as the most abundant ones or as those with the largest basins of attraction. On the other hand,…
Recently, non-reciprocal systems have become a focus of growing interest. Examples occur in soft and active matter, but also in engineered quantum materials and neural (brain) networks. Here, we investigate the impact of non-reciprocity on…
Time-reversal symmetry arises naturally as a structural property in many dynamical systems of interest. While the importance of hard-wiring symmetry is increasingly recognized in machine learning, to date this has eluded time-reversibility.…
We study the dynamical response of a circularly-driven rigid body, focusing on the description of intrinsic rotational behavior (reverse rotations). The model system we address is integrable but nontrivial, allowing for qualitative and…
Feedback is an essential composition operator in many classes of reactive and other systems. This paper studies feedback in the context of compositional theories with refinement. Such theories allow to reason about systems on a…
We illustrate a novel version of Willems' lemma for data-based representation of continuous-time systems. The main novelties compared to previous works are two. First, the proposed framework relies only on measured input-output trajectories…
Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is…
We provide a practical relaxation of Willems' fundamental lemma for discrete-time linear time-invariant (single-input-single-output) systems. Instead of maintaining conventional Willems' persistency of excitation condition in the behavioral…
Nonreciprocity originating from classical interactions among nonlinear scatterers has been attracting increasing attention in the quantum community, offering a promising tool to control excitation transfer for quantum information processing…
A theory of nonlinear signal propagation in multi-span wavelength division multiplexed coherent transmission systems that employ the semiconductor optical amplifier as in-line amplifiers is presented for the first time. The rigorous…
Systems that show different characteristics, such as finite-gain and passivity, depending on the nature of the inputs, are said to possess mixed input-output properties. In this paper, we provide a constructive method for characterizing…
Non-reciprocity and geometric frustration enable many-body systems to avoid crystalline order and instead exhibit complex, liquid-like behavior. Here we show that their interplay is richer than the sum of its parts, leading to surprising…
The collective chasing dynamics of non-reciprocally coupled densities leads to stable travelling waves which can be mapped to a model for emergent flocking. In this work, we couple the non-reciprocal Cahn-Hilliard model (NRCH) to a fluid to…
A possible approach to description of the non equilibrium system has been proposed. Based on the Fokker-Plank equation in term of energy for non equilibrium distribution function of macroscopical system was obtained the stationary solution…
An open stochastic system \`a la Jan Willems is a system affected by two qualitatively different kinds of uncertainty: one is probabilistic fluctuation, and the other one is nondeterminism caused by a fundamental lack of information. We…
This paper discusses the interplay of symmetries and stability in the analysis and control of nonlinear dynamical systems and networks. Specifically, it combines standard results on symmetries and equivariance with recent convergence…
Nonlinear optics has regained attention in recent years, especially in the context of optospintronics and topological materials. Nonlinear responses involved in various degrees of freedom manifest their intricacy more pronounced than linear…
The implications of the Lorentz reciprocity theorem for a scatterer connected to waveguides with arbitrary modes, including degenerate, evanescent, and complex modes, are discussed. In general it turns out that a matrix $CS$ is symmetric,…
Smillie (1984) proved an interesting result on the stability of nonlinear, time-invariant, strongly cooperative, and tridiagonal dynamical systems. This result has found many applications in models from various fields including biology,…