Related papers: A dynamically-consistent nonstandard finite differ…
We consider the homogeneous stochastic differential equation with unknown parameter to be estimated. We prove that the standard maximum likelihood estimate is strongly consistent under very mild conditions. There are also established the…
Discovery of dynamical systems from data forms the foundation for data-driven modeling and recently, structure-preserving geometric perspectives have been shown to provide improved forecasting, stability, and physical realizability…
Dynamic systems are ubiquitous in nature and are used to model many processes in biology, chemistry, physics, medicine, and engineering. In particular, systems of ordinary differential equations are commonly used for the mathematical…
In the context of a pandemic like COVID-19, and until most people are vaccinated, proactive testing and interventions have been proved to be the only means to contain the disease spread. Recent academic work has offered significant evidence…
This paper reinterprets the Synthetic Control (SC) framework through the lens of weighting philosophy, arguing that the contrast between traditional SC and Difference-in-Differences (DID) reflects two distinct modeling mindsets: sparse…
In the context of mathematical modeling, it is sometimes convenient to integrate models of different nature. These types of combinations, however, might entail difficulties even when individual models are well-understood, particularly in…
For a network of interconnected nonlinear dynamical systems an adaptive leader-follower output feedback synchronization problem is considered. The proposed structure of decentralized controller and adaptation algorithm is based on…
This study focuses on analyzing a deterministic SIR model governing the dynamics of the hosts and vectors on an urban network. Our analysis scrutinizes the typical existence--stability of the equilibria as well as the sensitivity of the…
A space discrete approximation to a highly nonlinear reaction-diffusion system endowed with a stochastic dynamical boundary condition is analyzed and the convergence of the discrete scheme to the solution to the corresponding continuum…
The worldwide spread of COVID-19 has called for fast advancement of new modelling strategies to estimate its unprecedented spread. Here, we introduce a model based on the fundamental SIR equations with a stochastic disorder by a random…
Inferring causal relationships as directed acyclic graphs (DAGs) is an important but challenging problem. Differentiable Causal Discovery (DCD) is a promising approach to this problem, framing the search as a continuous optimization. But…
This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
Dynamical properties of tropically discretized and max-plus negative feedback models are investigated. Reviewing the previous study [S. Gibo and H. Ito, J. Theor. Biol. 378, 89 (2015)], the conditions under which the Neimark-Sacker…
In this paper we propose a model predictive control scheme for constrained fractional-order discrete-time systems. We prove that all constraints are satisfied at all time instants and we prescribe conditions for the origin to be an…
In this paper, an epidemic model with spatial dependence is studied and results regarding its stability and numerical approximation are presented. We consider a generalization of the original Kermack and McKendrick model in which the size…
In this paper, the convergence of the solutions for a discretized linear state-based static peridynamic system to the corresponding continuous solution is analytically proven. To obtain an implementable model, we further apply…
In this paper we prove the existence of solutions for a class of viscoelastic dynamic systems on time--dependent cracked domains, with possibly degenerate viscosity coefficients. Under stronger regularity assumptions we also show a…
Dynamic feedback linearization-based methods allow us to design control algorithms for a fairly large class of nonlinear systems in continuous time. However, this feature does not extend to their sampled counterparts, i.e., for a given…
We present a new time discretization scheme adapted to the structure of GENERIC systems. The scheme is variational in nature and is based on a conditional incremental minimization. The GENERIC structure of the scheme provides stability and…