Related papers: Predictive dynamical and stochastic systems
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
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…
The paper is focused on the discussion of the phenomenon of transitional chaos in dynamic autonomous and non-autonomous systems. This phenomenon involves the disappearance of chaotic oscillations in specific time periods and the system…
The dynamics of a system formed by a finite number $N$ of globally coupled bistable oscillators and driven by external forces is studied focusing on a global variable defined as the arithmetic mean of each oscillator variable. Several…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
We study an extended system that without noise shows a monostable dynamics, but when submitted to an adequate multiplicative noise, an effective bistable dynamics arise. The stochastic resonance between the attractors of the…
Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic…
We study the impact of stochastic perturbations to deterministic dynamical systems using the formalism of the Ruelle response theory and explore how stochastic noise can be used to explore the properties of the underlying deterministic…
We identify an issue in recent approaches to learning-based control that reformulate systems with uncertain dynamics using a stochastic differential equation. Specifically, we discuss the approximation that replaces a model with fixed but…
In animal groups, individual decisions are best characterised by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so called intrinsic…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…
Many regenerative arguments in stochastic processes use random times which are akin to stopping times, but which are determined by the future as well as the past behaviour of the process of interest. Such arguments based on "conditioning on…
Learning stochastic models of dynamical systems from observed data is of interest in many scientific fields. Here, we propose a new method for this task within the family of dynamical variational autoencoders. The proposed double projection…
We consider stochastic dynamical systems defined by differential equations with a uniform random time delay. The latter equations are shown to be equivalent to deterministic higher-order differential equations: for an $n$-th order equation…
Some systems cannot be predicted by classical theories and it is required the development of combined deterministic and stochastic theories that make used of noise for dynamical prediction. Noise is not always an interfering signal which…
Stochastic differential equations describe well many physical, biological and sociological systems, despite the simplification often made in their derivation. Here the usage of simple stochastic differential equations to characterize and…
We present the observation that the process of stochastic model predictive control can be formulated in the framework of iterated function systems. The latter has a rich ergodic theory that can be applied to study the system's long-run…
Demographic noise has profound effects on evolutionary and population dynamics, as well as on chemical reaction systems and models of epidemiology. Such noise is intrinsic and due to the discreteness of the dynamics in finite populations.…
The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces a variant of stochastic interpolation (SI) for probabilistic…
Recent research has provided a wealth of evidence highlighting the pivotal role of high-order interdependencies in supporting the information-processing capabilities of distributed complex systems. These findings may suggest that high-order…