Related papers: A continuation approach to computing phase resetti…
Causal inference in continuous-time sequential decision problems is challenged by hidden confounders. We show that, in latent state-space models with time-varying interventions, observability of the latent dynamics from observed data is…
Resetting is a renewal mechanism in which a process is intermittently repeated after a random or fixed time. This simple act of stop and repeat profoundly influences the behaviour of a system as exemplified by the emergence of…
Spontaneous oscillations induced by time delays are observed in many real-world systems. Phase reduction theory for limit-cycle oscillators described by delay-differential equations (DDEs) has been developed to analyze their synchronization…
Neural synchronization is believed to be critical for many brain functions. It frequently exhibits temporal variability, but it is not known if this variability has a specific temporal patterning. This study explores these…
We study a noisy oscillator with pulse delayed feedback, theoretically and in an electronic experimental implementation. Without noise, this system has multiple stable periodic regimes. We consider two types of noise: i) phase noise acting…
Synchronization in quantum systems has been recently studied through persistent oscillations of local observables, which stem from undamped modes of the dissipative dynamics. However, the existence of such modes requires fine-tuning the…
Rhythmic behaviors in neural systems often combine features of limit cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics (extended dwell times in localized regions of phase space).…
Accurate phase estimation -- the process of assigning phase values between $0$ and $2\pi$ to repetitive or periodic signals -- is a cornerstone in the analysis of oscillatory signals across diverse fields, from neuroscience to robotics,…
The organization of interactions in complex systems can be described by networks connecting different units. These graphs are useful representations of the local and global complexity of the underlying systems. The origin of their…
Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state…
We study the effect of structured higher-order interactions on the collective behavior of coupled phase oscillators. By combining a hypergraph generative model with dimensionality reduction techniques, we obtain a reduced system of…
Control-based continuation (CBC) is an experimental method that can reveal stable and unstable dynamics of physical systems. It extends the path-following principles of numerical continuation to experiments, and provides systematic…
Neural firing is often subject to negative feedback by adaptation currents. These currents can induce strong correlations among the time intervals between spikes. Here we study analytically the interval correlations of a broad class of…
Chaos provides many interesting properties that can be used to achieve computational tasks. Such properties are sensitivity to initial conditions, space filling, control and synchronization. Chaotic neural models have been devised to…
The phase sensitivity curve or phase response curve (PRC) quantifies the oscillator's reaction to stimulation at a specific phase and is a primary characteristic of a self-sustained oscillatory unit. Knowledge of this curve yields a phase…
This paper introduces the novel class of modulated cyclostationary processes, a class of non-stationary processes exhibiting frequency coupling, and proposes a method of their estimation from repeated trials. Cyclostationary processes also…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
Ordinary differential equations (ODEs) can model the transition of cell states over time. Bifurcation theory is a branch of dynamical systems which studies changes in the behavior of an ODE system while one or more parameters are varied. We…
We present a unified approach to those observables of stochastic processes under reset that take the form of averages of functionals depending on the most recent renewal period. We derive solutions for the observables, and determine the…
The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…