Related papers: Stochastic calculus: application to dynamic bifurc…
The so-called level crossing analysis has been used to investigate the empirical data set. But there is a lack of interpretation for what is reflected by the level crossing results. The fractional Gaussian noise as a well-defined stochastic…
The seemingly stochastic transient dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference. In vitro neurons, on the other hand, exhibit a highly deterministic…
Recent studies of cortical neurons driven by fluctuating currents revealed cutoff frequencies for action potential encoding of several hundred Hz. Theoretical studies of biophysical neuron models have predicted a much lower cutoff frequency…
A dynamical system that undergoes a supercritical Hopf's bifurcation is perturbed by a multiplicative Brownian motion that scales with a small parameter $\epsilon$. The random fluctuations of the system at the critical point are studied…
Filtered Poisson processes are often used as reference models for intermittent fluc- tuations in physical systems. Such a process is here extended by adding a noise term, either as a purely additive term to the process or as a dynamical…
Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies. A computational analysis is conducted to…
Bistability generated via a pure noise-induced phase transition is reexamined from the view of bifurcations in macroscopic cumulant dynamics. It allows an analytical study of the phase diagram in more general cases than previous methods. In…
We present recent results on noise-induced transitions in a nonlinear oscillator with randomly modulated frequency. The presence of stochastic perturbations drastically alters the dynamical behaviour of the oscillator: noise can wash out a…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
We present time-resolved measurements of electron transport through a quantum dot. The measurements were performed using a nearby quantum point contact as a charge detector. The rates for tunneling through the two barriers connecting the…
We perform dynamical analysis on a stochastic Rosenzweig-MacArthur model driven by {\alpha}-stable L\'evy motion. We analyze the existence of the equilibrium points, and provide a clear illustration of their stability. It is shown that the…
Diverse complex dynamical systems are known to exhibit abrupt regime shifts at bifurcation points of the saddle-node type. The dynamics of most of these systems, however, have a stochastic component resulting in noise driven regime shifts…
The influence of small random perturbations on a deterministic dynamical system with a locally stable equilibrium is considered. The perturbed system is described by the It\^{o} stochastic differential equation. It is assumed that the noise…
We revisit a textbook example of a singularly perturbed nonlinear boundary-value problem. Unexpectedly, it shows a wealth of phenomena that seem to have been overlooked previously, including a pitchfork bifurcation in the number of…
One of the major challenges in neuroscience is to determine how noise that is present at the molecular and cellular levels affects dynamics and information processing at the macroscopic level of synaptically coupled neuronal populations.…
The phenomenon of critical slowing down (CSD) has played a key role in the search for reliable precursors of catastrophic regime shifts. This is caused by its presence in a generic class of bifurcating dynamical systems. Simple time-series…
We demonstrate that the information contained in the spike occurrence times of a population of neurons can be broken up into a series of terms, each of which reflect something about potential coding mechanisms. This is possible in the…
We consider the transport statistics of classical bistable systems driven by noise. The stochastic path integral formalism is used to investigate the dynamics and distribution of transmitted charge. Switching rates between the two stable…
This chapter considers the computational and statistical aspects of learning linear thresholds in presence of noise. When there is no noise, several algorithms exist that efficiently learn near-optimal linear thresholds using a small amount…
Stochastic biochemical and transport processes have various final outcomes, and they can be viewed as dynamic systems with multiple exits. Many current theoretical studies, however, typically consider only a single time scale for each…