Related papers: Characterizing mixed mode oscillations shaped by n…
Many systems are modulated by unknown slow processes. This hinders analysis in highly non-linear systems, such as excitable systems. We show that for such systems, if the input matches the sparse `spiky' nature of the output, the spiking…
We demonstrated experimentally canard induced mixed mode oscillations (MMO) in an excitable glow discharge plasma, and the results are validated through numerical solution of the FitzHugh Nagumo (FHN) model. When glow discharge plasma is…
We analyze a class of network motifs in which a short, two-node positive feed- back motif is inserted in a three-node negative feedback loop. We demonstrate that such networks can undergo a bifurcation to a state where a stable fixed point…
Biological neurons receive multiple noisy oscillatory signals, and their dynamical response to the superposition of these signals is of fundamental importance for information processing in the brain. Here we study the response of neural…
A lack of software reproducibility has become increasingly apparent in the last several years, calling into question the validity of scientific findings affected by published tools. Reproducibility issues may have numerous sources of error,…
We analyze general two-species stochastic models, of the kind generally used for the study of population dynamics. We show that the conditions for the stochastic (microscopic) model to display approximate sustained oscillatory behavior are…
Mesoscopic fluctuations reveal stochastic dynamics of molecules in both inanimate and living matter. We investigate how small-number fluctuations shape the collective dynamics of molecular motors using motile cilia as model system. We…
Large language models perform text generation through high-dimensional internal dynamics, yet the temporal organisation of these dynamics remains poorly understood. Most interpretability approaches emphasise static representations or causal…
Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed…
Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to…
This paper aims at the study of controllability properties and induced controllability metrics on complex networks governed by a class of (discrete time) linear decision processes with mul-tiplicative noise. The dynamics are given by a…
We study noise induced switching in systems far from equilibrium by using an underdamped micromechanical torsional oscillator driven into the nonlinear regime. Within a certain range of driving frequencies, the oscillator possesses two…
It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from…
A detailed study of the slow manifold of a model exhibiting mixed-mode oscillations is presented. A scenario for the emergence of mixed-mode states which does not involve phase locking on a 2-torus is constructed. We show that mixed-modes…
We study statistical inference for small-noise-perturbed multiscale dynamical systems under the assumption that we observe a single time series from the slow process only. We construct estimators for both averaging and homogenization…
The theory of mixed-feedback systems provides an effective framework for the design of robust and tunable oscillations in nonlinear systems characterized by interleaved fast positive and slow negative feedback loops. The goal of this paper…
Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically; and the frequency spectrum of this chemical fluctuation carries valuable information about the mechanism and the dynamics of the intracellular…
Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…
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…
We study statistical inference for small-noise-perturbed multiscale dynamical systems. We prove consistency, asymptotic normality, and convergence of all scaled moments of an appropriately-constructed maximum likelihood estimator (MLE) for…