Related papers: On the abrupt change of the maximum likelihood sta…
Transition phenomena between thermodynamic branch and turbulent branch in submarginal turbulent plasma are analyzed with statistical theory. Time-development of turbulent fluctuation is obtained by numerical simulations of Langevin equation…
Relaxation phenomena in glasses can be related to jump processes between different minima of the potential energy in the configuration space. These transitions play a key role in the low temperature regime, giving rise to tunneling systems…
The abrupt changes that are ubiquitous in physical and natural systems are often well characterized by shot noise with a state dependent recurrence frequency and jump amplitude. For such state dependent behavior, we derive the transition…
We consider an extension of the zero-range process to the case where the hop rate depends on the state of both departure and arrival sites. We recover the misanthrope and the target process as special cases for which the probability of the…
The maximum likelihood approach is adapted to the problem of estimation of drift and diffusion functions of stochastic processes from measured time series. We reconcile a previously devised iterative procedure [Kleinhans et al., Physics…
In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover it is regarded as a…
Many stochastic physical systems evolve smoothly over time in the sense that the distribution of states changes regularly across time steps. The transition from current state to the next state can often be modeled as the combination of a…
A general formulation of stochastic thermodynamics is presented for open systems exchanging energy and particles with multiple reservoirs. By introducing a partition in terms of "macrostates" (e.g. sets of "microstates"), the consequence on…
An abrupt climatic transition could be triggered by a single extreme event, an $\alpha$-stable non-Gaussian L\'evy noise is regarded as a type of noise to generate such extreme events. In contrast with the classic Gaussian noise, a…
In recent years, the discovery of complex dynamic systems in various fields through data-driven methods has attracted widespread attention. This method has played the role of data and has become an advantageous tool for us to study complex…
The ocean thermohaline circulation under uncertainty is investigated by a random dynamical systems approach. It is shown that the asymptotic dynamics of the thermohaline circulation is described by a random attractor and by a system with…
We consider the dynamics of a 1D system evolving according to a deterministic drift and randomly forced by two types of jumps processes, one representing an external, uncontrolled forcing and the other one a control that instantaneously…
Systems of stochastic particles evolving in a multi-well energy landscape and attracted to their barycenter is the prototypical example of mean-field process undergoing phase transitions: at low temperature, the corresponding mean-field…
Ecosystems often undergo abrupt regime shifts in response to gradual external changes. These shifts are theoretically understood as a regime switch between alternative stable states of the ecosystem dynamical response to smooth changes in…
We study the impact of Brownian noise on transitions between metastable equilibrium states in a stochastic ice sheet model. Two methods to accomplish different objectives are employed. The maximal likely trajectory by maximizing the…
Multistability is a phenomenon prevalent in many natural systems. In climate, for example, it allows the possibility of irreversible consequences on planetary scale as a result of climate change. Indeed, a climate ``tipping element'' is a…
A stochastic system under the influence of a stochastic environment is correlated with both present and future states of the environment. Such a system can be seen as implicitly implementing a predictive model of future environmental…
Maximum entropy (maxEnt) inference of state probabilities using state-dependent constraints is popular in the study of complex systems. In stochastic dynamical systems, the effect of state space topology and path-dependent constraints on…
We study a class of random processes on $N$ particles which can be interpreted as stochastic model of luminescence. Each particle can stay in one of two states: Excited state or ground state. Any particle at ground state is excited with a…
We examine what happens in a population when it experiences an abrupt change in surrounding conditions. Several cases of such "abrupt transitions" for both physical and living social systems are analyzed from which it can be seen that all…