Related papers: Stochastic Nonlinear Dynamics of Interpersonal and…

Modelling is an essential procedure in analyzing and controlling a given logical dynamic system (LDS). It has been proved that deterministic LDS can be modeled as a linear-like system using algebraic state space representation. However, due…

We develop a general theory dealing with stochastic models for dynamical systems that are governed by various nonlinear, ordinary or partial differential, equations. In particular, we address the problem how flows in the random medium…

Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…

In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…

The study of stochastic systems has received considerable interest over the years. Their dynamics can describe many equilibrium and nonequilibrium fluctuating systems. At the same time, nonequilibrium constraints interact with the time…

Proceeding from the concept of rational expectations, a new dynamic model of supply and demand in a single market with one supplier, one buyer, and one kind of commodity is developed. Unlike the cob-web dynamic theories with adaptive…

Dynamic heterogeneity has often been modeled by assuming that a single-particle observable, fluctuating at a molecular scale, is influenced by its coupling to environmental variables fluctuating on a second, perhaps slower, time scale.…

This research investigates the impact of dynamic, time-varying interactions on cooperative behaviour in social dilemmas. Traditional research has focused on deterministic rules governing pairwise interactions, yet the impact of interaction…

Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…

Emotional disorders and psychological flourishing are the result of complex interactions between positive and negative affects that depend on external events and the subject's internal representations. Based on psychological data, we…

Stochastic models play an essential role in accounting for the variability and unpredictability seen in real-world. This paper focuses on the application of the gamma distribution to analysis of the stationary distributions of populations…

Linear dynamical relations that may exist in continuous-time, or at some natural sampling rate, are not directly discernable at reduced observational sampling rates. Indeed, at reduced rates, matricial spectral densities of vectorial time…

Conventional studies of biomolecular behaviors rely largely on the construction of kinetic schemes. Since the selection of these networks is not unique, a concern is raised whether and under which conditions hierarchical schemes can reveal…

In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…

Many intelligent user interfaces employ application and user models to determine the user's preferences, goals and likely future actions. Such models require application analysis, adaptation and expansion. Building and maintaining such…

The concept of stochastic Lagrangian and its use in statistical dynamics is illustrated theoretically, and with some examples. Dynamical variables undergoing stochastic differential equations are stochastic processes themselves, and their…

In this paper, we study connections between the classical model-based approach to nonlinear system theory, where systems are represented by equations, and the nonlinear behavioral approach, where systems are defined as sets of trajectories.…

Recent experiments have demonstrated the ability to manipulate nonlinear interactions via time modulation, giving rise to the so-called stroboscopic nonlinearity. To date, however, this phenomenon has not been subjected to a rigorous…