Related papers: An algorithm for finding weakly reversible deficie…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
Verification of discrete time or continuous time dynamical systems over the reals is known to be undecidable. It is however known that undecidability does not hold for various classes of systems: if robustness is defined as the fact that…
Understanding the dynamics of complex systems is a central task in many different areas ranging from biology via epidemics to economics and engineering. Unexpected behaviour of dynamic systems or even system failure is sometimes difficult…
Stochastic dynamical systems often contain nonlinearities which make it hard to compute probability density functions or statistical moments of these systems. For the moment computations, nonlinearities in the dynamics lead to unclosed…
In this paper we present an algorithmic procedure that transforms, if possible, a given system of ordinary or partial differential equations with radical dependencies in the unknown function and its derivatives into a system with polynomial…
We consider continuous-time dynamics for distributed optimization with set constraints in the paper. To handle the computational complexity of projection-based dynamics due to solving a general quadratic optimization subproblem with…
A system of nonlinear ordinary differential equations with forcing function is developed to model evolution processes in complex systems. In this system R, C, and P are the resource, consumption, and production functions correspondingly. F…
An alternative numerical method is developed to find stable and unstable periodic orbits of nonlinear dynamical systems. The method exploits the high-efficiency of the Levenberg-Marquardt algorithm for medium-sized problems and has the…
Stabilizing an unknown control system is one of the most fundamental problems in control systems engineering. In this paper, we provide a simple, model-free algorithm for stabilizing fully observed dynamical systems. While model-free…
In recent work [Coretti et al., The Journal of Chemical Physics, 2018, 149, 191102], a new algorithm to solve numerically the dynamics of the shell model for polarization was presented. The approach, broadly applicable to systems involving…
In this paper, a continuous approximation to studying a class of PWC systems of fractionalorder is presented. Some known results of set-valued analysis and differential inclusions are utilized. The example of a hyperchaotic PWC system of…
Designing control policies whose performance level is guaranteed to remain above a given threshold in a span of environments is a critical feature for the adoption of reinforcement learning (RL) in real-world applications. The search for…
Computation biology helps to understand all processes in organisms from interaction of molecules to complex functions of whole organs. Therefore, there is a need for mathematical methods and models that deliver logical explanations in a…
Analytical work probability distributions for open classical systems are scarce; they can only be calculated in a few examples. In this work, I present a new method to derive such quantities for weakly driven processes in the overdamped…
This paper studies the relations among system parameters, uniqueness, and stability of equilibria, for kinetic systems given in the form of polynomial ODEs. Such models are commonly used to describe the dynamics of nonnegative systems, with…
We analyze a power distribution line with high penetration of distributed generation and strong variations of power consumption and generation levels. In the presence of uncertainty the statistical description of the system is required to…
In this paper, we prove several theorems on systems of polynomials with at least one positive real zero based on the theory of conceive polynomials. These theorems provide sufficient conditions for systems of multivariate polynomials…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…
This paper leverages recent advances in high derivatives reconstruction from noisy-time series and sparse multivariate polynomial identification in order to improve the process of parsimoniously identifying, from a small amount of data,…