Related papers: Dynamical noise can enhance high-order statistical…

The counterintuitive emergence of order from noise is a central phenomenon in science, ranging from pattern formation and synchronization to order-by-disorder in frustrated systems. While large-scale spatial self-organization induced by…

Neural-network models of high-level brain functions such as memory recall and reasoning often rely on the presence of stochasticity. The majority of these models assumes that each neuron in the functional network is equipped with its own…

Noise-induced phenomena in high-dimensional dynamical systems were investigated from a random dynamical systems point of view. In a class of generalized H\'enon maps, which are randomly perturbed delayed logistic maps, with monotonically…

Noisy fluctuations are ubiquitous in complex systems. They play a crucial or delicate role in the dynamical evolution of gene regulation, signal transduction, biochemical reactions, among other systems. Therefore, it is essential to…

Based on a non-equilibrium mechanism for spatial pattern formation we study how position information can be controlled by locally coupled discrete dynamical networks, similar to gene regulation networks of cells in a developing…

Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…

Can noise be beneficial to machine-learning prediction of chaotic systems? Utilizing reservoir computers as a paradigm, we find that injecting noise to the training data can induce a stochastic resonance with significant benefits to both…

Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…

We study a system whose dynamics are governed by predictions of its future states. A general formalism and concrete examples are presented. We find that the dynamical characteristics depend on how to shape the predictions as well as on how…

We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the…

Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…

This Thesis explores how tools from Statistical Physics and Information Theory can help us describe and understand complex systems. In the first part, we study the interplay between internal interactions, environmental changes, and…

Complex systems are often characterized by the interplay of multiple interconnected dynamical processes operating across a range of temporal scales. This phenomenon is widespread in both biological and artificial scenarios, making it…

Complex systems with global interactions tend to be stable if interactions between components are sufficiently homogeneous. In biological systems, which often have small copy numbers and interactions mediated by diffusing agents, noise and…

The studies of collective oscillations induced by higher-order interactions point out the necessity of group effect in coupling modelization. As yet the related advances are mainly concentrated on nonlinear coupling patterns and cannot be…

Cooperative effects of periodic force and noise in globally Cooperative effects of periodic force and noise in globally coupled systems are studied using a nonlinear diffusion equation for the number density. The amplitude of the order…

Under normal operations, memristive devices undergo variability in time and space and have internal dynamics. Interplay of memory and stochastic signal processing in memristive devices makes them candidates for performing bio-inspired tasks…

Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

Self-organized systems, from synthetic nanostructures to developing organisms, are composed of fluctuating units capable of forming robust functional structures despite noise. Here, we ask: are there fundamental bounds on the robustness of…