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Efficiently exploiting servers in data centers requires performance analysis methods that account not only for the stochastic nature of demand but also for server heterogeneity. Although several recent works proved optimality results for…
Stable limit cycle as a stabilized mechanical oscillation is the primary result of the dynamical evolution of an optomechanical system under sufficiently powerful pump. Because this dynamical process is highly nonlinear, it was not clear…
We propose and study a stochastic capital-labour model with logistic growth function. First, we show that the model has a unique positive global solution. Then, using the Lyapunov analysis method, we obtain conditions for the extinction of…
This work is focused on the doubly nonlinear equation, whose solutions represent the bending motion of an extensible, elastic bridge suspended by continuously distributed cables which are flexible and elastic with stiffness k^2. When the…
This paper presents a novel framework for stabilizing nonlinear systems represented in state-dependent form. We first reformulate the nonlinear dynamics as a state-dependent parameter-varying model and synthesize a stabilizing controller…
We consider nonlinear Schrodinger equations with either local or nonlocal nonlinearities. In addition, we include periodic potentials as used, for example, in matter wave experiments in optical lattices. By considering the corresponding…
We present a macroeconomic agent-based model that combines several mechanisms operating at the same timescale, while remaining mathematically tractable. It comprises enterprises and workers who compete in a job market and a commodity goods…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
This study investigates two models of varying complexity for optimizing intraday arbitrage energy trading of a battery energy storage system using a model predictive control approach. Scenarios reflecting different stages of the system's…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
We analyze export data aggregated at world global level of 219 classes of products over a period of 39 years. Our main goal is to set up a dynamical model to identify and quantify plausible mechanisms by which the evolutions of the various…
In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…
A re-entrant manufacturing system producing a large number of items and involving many steps can be approximately modeled by a hyperbolic partial differential equation (PDE) according to mass conservation law with respect to a continuous…
Assemble-to-order approaches deal with randomness in demand for end items by producing components under uncertainty, but assembling them only after demand is observed. Such planning problems can be tackled by stochastic programming, but…
A formula of grain growth rate, based on a nonlinear capillarity-driven relation, is derived to predict and interpret realistic growth processes in polycrystalline systems. The derived formula reveals how the growth and stagnation of grains…
Obtaining initial conditions and parameterizations leading to a model consistent with available measurements or safety specifications is important for many applications. Examples include model (in-)validation, prediction, fault diagnosis,…
We address a novel approach for stochastic individual-based modelling of a single species population. Individuals are distinguished by their remaining lifetimes, which are regulated by the interplay between the inexorable running of time…
Effort has been given for the development of an analytical approach that helps to address several sigmoidal and non-sigmoidal growth processes found in literature. In the proposed approach, the role of specific growth rate in different…
The logistic equation has been extensively used to model biological phenomena across a variety of disciplines and has provided valuable insight into how our universe operates. Incorporating time-dependent parameters into the logistic…
While the identification of nonlinear dynamical systems is a fundamental building block of model-based reinforcement learning and feedback control, its sample complexity is only understood for systems that either have discrete states and…