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We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…
Learning in living organisms is typically associated with networks of neurons. The use of large numbers of adjustable units has also been a crucial factor in the continued success of artificial neural networks. In light of the complexity of…
The paper documents the implementation of a novel phase-noise analysis module within the open-source QUCS circuit simulator environment. The underlying algorithm is based on a rigorous, unified time-domain methodology of (coupled)…
Recurrent networks of dynamic elements frequently exhibit emergent collective oscillations, which can display substantial regularity even when the individual elements are considerably noisy. How noise-induced dynamics at the local level…
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent…
The design of biological systems is hindered by uncertainty arising from both intrinsic stochasticity of biomolecular reactions and variability across laboratory or experimental conditions. In this work, we present a sequential framework to…
Complex networks are abundant in nature and many share an important structural property: they contain a few nodes that are abnormally highly connected (hubs). Some of these hubs are called influencers because they couple strongly to the…
Using a stochastic nonlinear phase oscillator model, we study the effect of event-triggered feedback on the statistics of interevent intervals. Events are associated with the entering of a new cycle. The feedback is modeled by an…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
Models of coupled oscillators are useful in describing a wide variety of phenomena in physics, biology and economics. These models typically rest on the premise that the oscillators are weakly coupled, meaning that amplitudes can be assumed…
In complex networks, interactions between multiple agents give rise to an array of intricate global dynamics, ranging from synchronization to cluster formations. Decoding the connectivity structure as well as the types of interactions from…
We perform experiments and phase model simulations with a ring network of oscillatory electrochemical reactions to explore the effect of random connections and non-isochronocity of the interactions on the pattern formation. A few additional…
A circuit architecture is proposed and implemented for a dynamical network composed of a type of hybrid chaotic oscillator based on Unstable Dissipative Systems (UDS). The circuit architecture allows selecting a network topology with its…
Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now…
Non-reciprocal interactions in elastic media give rise to rich non-equilibrium behaviors, but controllable experimental realizations of such odd elastic phenomena remain scarce. Building on recent breakthroughs in electrical analogs of…
We develop a framework for the general interpretation of the stochastic dynamical system near a limit cycle. Such quasi-periodic dynamics are commonly found in a variety of nonequilibrium systems, including the spontaneous oscillations of…
Electric circuits manipulate electric charge and magnetic flux via a small set of discrete components to implement useful functionality over continuous time-varying signals represented by currents and voltages. Much of the same…
Quantum coherent feedback has been proven to be an efficient way to tune the dynamics of quantum optical systems and, recently, those of solid-state quantum circuits. Here, inspired by the recent progress of quantum feedback experiments,…
Some biological systems operate at the critical point between stability and instability and this requires a fine-tuning of parameters. We bring together two examples from the literature that illustrate this: neural integration in the…
Autonomous sustained oscillations are ubiquitous in living and nonliving systems. As open systems, far from thermodynamic equilibrium, they defy entropic laws which mandate convergence to stationarity. We present structural conditions on…