Related papers: Inference of stochastic nonlinear oscillators with…
A new approach to nonlinear modelling is presented which, by incorporating the global behaviour of the model, lifts shortcomings of both least squares and total least squares parameter estimates. Although ubiquitous in practice, a least…
In the following, we discuss nonlinear simulations of nonlinear dynamical systems, which are applied in technical and biological models. We deal with different ideas to overcome the treatment of the nonlinearities and discuss a novel…
We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D.A. Smirnov and B.P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely…
Phase response curves are important for analysis and modeling of oscillatory dynamics in various applications, particularly in neuroscience. Standard experimental technique for determining them requires isolation of the system and…
We propose a method for learning linear models whose predictive performance is robust to causal interventions on unobserved variables, when noisy proxies of those variables are available. Our approach takes the form of a regularization term…
Classical spin models with discrete or continuous degrees of freedom arise in many studies of complex physical systems. A wide class of hard real-life optimisation problems can be formulated as a minimisation of a spin Hamiltonian. Here we…
Ordinary differential equation models are used to describe dynamic processes across biology. To perform likelihood-based parameter inference on these models, it is necessary to specify a statistical process representing the contribution of…
A new model for time series with a specific oscillation pattern is proposed. The model consists of a hidden phase process controlling the speed of polling and a nonparametric curve characterizing the pattern, leading together to a…
This paper discusses a general framework for designing robust state estimators for a class of discrete-time nonlinear systems. We consider systems that may be impacted by impulsive (sparse but otherwise arbitrary) measurement noise…
The modeling of intrinsic noise in pulsar timing residual data is of crucial importance for Gravitational Wave (GW) detection and pulsar timing (astro)physics in general. The noise budget in pulsars is a collection of several well studied…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network…
We formulate a phase-reduction method for a general class of noisy limit cycle oscillators and find that the phase equation is parametrized by the ratio between time scales of the noise correlation and amplitude relaxation of the limit…
In this study, we estimate parameters in stochastic oscillatory systems by developing a novel cost function. This function incorporates power spectral density, analytic signal, and position crossings, each weighted to capture distinct…
A new type of noised-induced phase transitions that should occur in systems of elements with motivated behavior is considered. By way of an example, a simple oscillatory system {x,v} with additive white noise is analyzed numerically. A…
The dynamical control of energy transfer between interacting systems is fundamental in diverse applications related to physical, electronic and chemical processes. Recent developments show that noise may enhance or suppress power transfer…
Many physical, chemical and biological processes rely on intrinsic oscillations to employ resonance responses to external stimuli of certain frequency. Such resonance phenomena in biological systems are typically explained by one of two…
In the presence of interactions the frequency of a simple harmonic oscillator deviates from the noninteracting one. Various methods can be used to compute the changes to the frequency perturbatively. Some of them resemble the methods used…
Using Kalman techniques, it is possible to perform optimal estimation in linear Gaussian state-space models. We address here the case where the noise probability density functions are of unknown functional form. A flexible Bayesian…
The paper deals with the problem of output regulation of nonlinear systems by presenting a learning-based adaptive internal model-based design strategy. We borrow from the adaptive internal model design technique recently proposed in [1]…