Related papers: Bounds on the state vector growth rate in stochast…
This article concerns the performance limits of strictly causal state estimation for linear systems with fixed, but uncertain, parameters belonging to a finite set. In particular, we provide upper and lower bounds on the smallest achievable…
In the data-based setting, analysis and control design of dynamical systems using measured data are typically based on overlapping trajectory segments of the input and output variables. This could lead to complex designs because the system…
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using the full model of the problem requires initial values for…
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of…
We establish global stability for a chemotaxis-growth model with logarithmic sensitivity under dynamic Dirichlet boundary conditions on a 1D domain. We analyze both parabolic-parabolic and parabolic-hyperbolic systems. The key challenge is…
The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in…
Local expansion exponents for nonequilibrium dynamical systems, described by partial differential equations, are introduced. These exponents show whether the system phase volume expands, contracts, or is conserved in time. The ways of…
This paper introduces a new method for assessing the boundedness and stability of certain vector nonlinear systems with delays and variable coefficients. The approach is based on developing scalar counterparts to the given vector systems.…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
This study deals with continuous limits of interacting one-dimensional diffusive systems, arising from stochastic distortions of discrete curves with various kinds of coding representations. These systems are essentially of a…
We study the spread of a novel state in a network, in the presence of an exogenous control. The considered controlled evolutionary dynamics is a non-homogeneous Markov process that describes the evolution of the states of all nodes in the…
Finding the stochastic equilibria for finite-state stochastic matrices amounts to solving an eigen\-vector problem $\pi = \pi P$. Various techniques for doing so are known, some extremely computationally intensive. Herein we shall aim to…
This paper proposes a framework to ensure the existence of dynamical system trajectories in the state space of labeled, weighted, and attributed graphs. The evolution of such a system exhibits hybrid behavior: discrete jumps affecting the…
Statistical mechanics has grown without bounds in space. Statistical mechanics of point particles in an unbounded perfect gas is commonly accepted as a foundation for understanding many systems, including liquids like the concentrated salt…
We study the asymptotic behavior of continuous-time, time-inhomogeneous Markovian quantum dynamics in a stationary random environment. Under mild faithfulness and eventually positivity-improving assumptions, the normalized evolution…
We prove a maximal velocity bound for the dynamics of Markovian open quantum systems. The dynamics are described by one-parameter semi-groups of quantum channels satisfying the von Neumann-Lindblad equation. Our result says that dynamically…
The paper aims to discuss statistical properties of the multi-agent based model of competitive growth. Each of the agents is described by growth (or decay) rule of its virtual "mass" with the rate affected by the interaction with other…
The Einstein evolution equations may be written in a variety of equivalent analytical forms, but numerical solutions of these different formulations display a wide range of growth rates for constraint violations. For symmetric hyperbolic…
We analyze the dynamics of streaming stochastic gradient descent (SGD) in the high-dimensional limit when applied to generalized linear models and multi-index models (e.g. logistic regression, phase retrieval) with general data-covariance.…
In this paper it is showed that if a time-varying uncertain system is robustly completely detectable then there exists an estimator for this system, i.e. we can estimate asymptotically the state vector of the system. Moreover, if a…