Related papers: Transience in Dynamical Systems
This paper is a preliminary work to address the problem of dynamical systems with parameters varying in time. An idea to predict their behaviour is proposed. These systems are called \emph{transient systems}, and are distinguished from…
Development of theory of dynamical systems admitting the normal shift in 1993-1999 is reviewed. Basics are given with complete proofs.
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
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…
A universal definition of non-Markovianity for open systems dynamics is proposed. It is extended from the classical definition to the quantum realm by showing that a `transition' from the Markov to the non-Markov regime occurs when the…
We prove a transient fluctuation theorem for the currents for continuous-time Markov jump processes with stationary rates, generalizing an asymptotic result by Andrieux and Gaspard [J. Stat. Phys. 127, 107 (2007)] to finite times. The…
Markov diagrams provide a way to understand the structures of topological dynamical systems. We examine the construction of such diagrams for subshifts, including some which do not have any nontrivial Markovian part, in particular Sturmian…
Dissipative phase transitions in quantum systems have been largely studied under the so-called Markovian approximation, where the environments to which the systems are coupled are memoryless. Here, we present a generalization of the…
We study the Markovianity of a composite system and its subsystems. We show how the dissipative nature of a subsystem's dynamics can be modified without having to change properties of the composite system environment. By preparing different…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and…
We construct a large class of non-Markovian master equations that describe the dynamics of open quantum systems featuring strong memory effects, which relies on a quantum generalization of the concept of classical semi-Markov processes.…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
Non-autonomous dynamical systems help us to understand the implications of real systems which are in contact with their environment as it actually occurs in nature. Here, we focus on systems where a parameter changes with time at small but…
We have earlier constructed a generalized entropy concept to show the direction of time in an evolution following from a Markov generator. In such a dynamical system, the entity found changes in a monotonic way starting from any initial…
Transitions between steady dynamical regimes in diverse applications are often modelled using discontinuities, but doing so introduces problems of uniqueness. No matter how quickly a transition occurs, its inner workings can affect the…
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…
We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole…