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Oscillations in nonequilibrium noisy systems are important physical phenomena. These oscillations can happen in autonomous biochemical oscillators such as circadian clocks. They can also manifest as subharmonic oscillations in periodically…

Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…

We study the ability of neural networks to calculate feedback control signals that steer trajectories of continuous time non-linear dynamical systems on graphs, which we represent with neural ordinary differential equations (neural ODEs).…

We describe a mechanism for pronounced biochemical oscillations, relevant to microscopic systems, such as the intracellular environment. This mechanism operates for reaction schemes which, when modeled using deterministic rate equations,…

Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesize that some symptoms originate from the inability to spontaneously transition from…

Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…

We analyze the properties of a quantum system composed of two coherently coupled quantum oscillators and show through simulations that it fulfills the two properties required for reservoir computing: non-linearity and fading memory. We…

Surrogate modeling of non-linear oscillator networks remains challenging due to discrepancies between simplified analytical models and real-world complexity. To bridge this gap, we investigate hybrid reservoir computing, combining reservoir…

Building mathematical models of brains is difficult because of the sheer complexity of the problem. One potential starting point is through basal cognition, which gives abstract representation of a range of organisms without central nervous…

Many natural systems including the brain comprise coupled non-uniformly stimulated elements. In this paper we show that heterogeneously driven networks of excitatory-inhibitory units exhibit striking collective phenomena, including…

We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact…

Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…

Most complex systems are nonlinear, relying on emergent behavior from interacting subsystems, often characterized by oscillatory dynamics. Collective oscillatory behavior is essential for the proper functioning of many real world systems.…

Today's deep learning architectures are primarily based on perceptron models, which do not capture the oscillatory dynamics characteristic of biological neurons. Although oscillatory systems have recently gained attention for their closer…

In the present work, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system…

For many natural and engineered systems, a central function or design goal is the synchronization of one or more rhythmic or oscillating processes to an external forcing signal, which may be periodic on a different time-scale from the…

A set of Hamiltonians that are not self-adjoint but have the spectrum of the harmonic oscillator is studied. The eigenvectors of these operators and those of their Hermitian conjugates form a bi-orthogonal system that provides a…

Noise can induce coherent oscillations in excitable systems without periodic orbits. Here, we establish a method to derive a hybrid system approximating the noise-induced coherent oscillations in excitable systems and further perform phase…

Many biological systems can sense periodical variations in a stimulus input and produce well-timed, anticipatory responses after the input is removed. Such systems show memory effects for retaining timing information in the stimulus and…

In this study, we investigate the continuous time dynamics of Recurrent Neural Networks (RNNs), focusing on systems with nonlinear activation functions. The objective of this work is to identify conditions under which RNNs exhibit perpetual…