We discuss different approaches for the analytical description of a mechanical system used in control theory, aiming at the analytical modelling of experimental artefacts observed in the implementation of ideal searched trajectories. Starting from an...
In recent years, we have witnessed the emergence of the implementation and integration of significant working solutions in transportation, especially within the smart city concept. A lot of cities in Europe and around the world support this initiativ...
In this paper, we introduce two new methods to solve systems of ordinary differential equations. The first method is constituted of the generalized Bernstein functions, which are obtained by Bernstein polynomials, and operational matrix of differenti...
This paper deals with the stabilization of a class of uncertain nonlinear ordinary differential equations (ODEs) with a dynamic controller governed by a linear
Optical density (OD) is a critical process parameter during fermentation, this being directly related to cell density, which provides valuable information regarding the state of the process. However, to measure OD, sampling of the fermentation broth...
Neural Ordinary Differential Equations (Neural ODEs) have emerged as a promising approach for learning the continuous-time behaviour of dynamical systems from data. However, Neural ODEs are black-box models, posing challenges in interpreting and unde...
Noether symmetries and first integrals of a class of two-dimensional systems of second order ordinary differential equations (ODEs) are investigated using real and complex methods. We show that first integrals of systems of two second order ODEs deri...
Given an autonomous second-order ordinary differential equation (ODE), we define a Riemannian metric on an open subset of the first-order jet bundle. A relationship is established between the solutions of the ODE and the geodesic curves with respect...
A new method of numerical integration for a perturbed and damped systems of linear second-order differential equations is presented. This new method, under certain conditions, integrates, without truncation error, the IVPs (initial value problems) of...
In this article, we focus on the acceleration of a chemical reaction simulation that relies on a system of stiff ordinary differential equation (ODEs) targeting heterogeneous computing systems with CPUs and field-programmable gate arrays (FPGAs). Spe...
This work addresses the spread of a disease within an urban system, definedas a network of interconnected cities. The first step consists of comparing two differentapproaches: a macroscopic one, based on a system of coupled Ordinary DifferentialEquatio...
Multistep methods for the numerical solution of ordinary differential equations are an important class of applied mathematical techniques. This paper is motivated by recently reported advances in semi-implicit numerical integration methods, multistep...
In this work, we derived an Abel–Jacobi–Liouville identity for the case of two-dimensional linear systems of ODEs (ordinary differential equations) with reflection. We also present a conjecture for the general case and an application to coupled harmo...
A mathematical model consisting of weakly coupled time fractional one parabolic PDE and one ODE equations describing dynamical processes in porous media is our physical motivation. As is often performed, by solving analytically the ODE equation, such...
In this paper we study an ODE model for the interaction between nature and society where the system dynamics is driven largely by the social wealth. The relevant variables are renewable resources, non-renewable ones, and wealth, while population depe...
The necessity of a flow express control of oil dispersed system (ODS) properties, such as crude oil, oil products, water–oil emulsions, and polluted waters, is substantiated. This control is necessary for the production and preparation of oil f...
We consider in this article the stochastic fractional Zakharov system derived by the multiplicative Wiener process in the Stratonovich sense. We utilize two distinct methods, the Riccati–Bernoulli sub-ODE method and Jacobi elliptic function met...
Solving ordinary differential equations (ODE) on heterogenous or multi-core/parallel embedded systems does significantly increase the operational capacity of many sensing systems in view of processing tasks such as self-calibration, model-based measu...
In this paper, we introduce an ODE system to model the interaction between natural resources and human exploitation in a rich consumeristic society. In this model, the rate of change in population depends on wealth per capita, and the rate of consump...
We consider a system of two differential equations modeling chemotaxis. The system consists of a parabolic equation describing the behavior of a biological species “u” coupled to an ODE patterning the concentration of a chemical substance...
Predicting short-term passenger flow accurately is of great significance for daily management and for a timely emergency response of rail transit networks. In this paper, we propose an attention-based Graph–Temporal Fused Neural Network (GTFNN)...
This paper is concerned with solving the problem of identifying the control vector problem for a fractional multi-order system of nonlinear ordinary differential equations (ODEs). We describe a quasilinearization approach, based on minimization of a...
Changes in diet are heavily associated with high mortality rates in several types of cancer. In this paper, a new mathematical model of tumor cells growth is established to dynamically demonstrate the effects of abnormal cell progression on the cells...
Traffic congestion is an important problem faced by Intelligent Transportation Systems (ITS), requiring models that allow predicting the impact of different solutions on urban traffic flow. Such an approach typically requires the use of simulations,...
In this work, we investigate an ODE system designed to describe the interplay between human society and the environment, with a strong focus on the role of non-renewable resources. Specifically, our model captures how the depletion and replenishment...
We consider an inverse problem of recovering the mortality rate in the honey bee difference equation model, that tracks a forage honeybee leaving and entering the hive each day. We concentrate our analysis to the model without pesticide contamination...
The Kuralay-II system (K-IIS) plays a pivotal role in modeling sophisticated nonlinear wave processes, particularly in the field of optics. This study introduces novel soliton solutions for the K-IIS, derived using the Riccati–Bernoulli sub-ODE...
The purpose of this paper is threefold: (i) to highlight the second order ordinary differential equations (ODEs) as generated by flows and Riemannian metrics (decomposable single-time dynamics); (ii) to analyze the second order partial differential e...
A Hermite fitted block integrator (HFBI) for numerically solving second-order anisotropic elliptic partial differential equations (PDEs) was developed, analyzed, and implemented in this study. The method was derived through collocation and interpolat...
This article considers heat transfer in a solid body with temperature-dependent thermal conductivity that is in contact with a tank filled with liquid. The liquid in the tank is heated by hot liquid entering the tank through a pipe. Liquid at a lower...
Frequency stability becomes more and more important with the increase in inverter-based resources in power systems. To enhance the frequency stability, this paper proposes a novel data-driven method for frequency stability assessment and control for...
Traffic simulation is essential for evaluating transportation policies, infrastructure changes, and mixed traffic scenarios with human-driven and autonomous vehicles, yet its reliability critically depends on accurate calibration of origin–dest...
The fractional PDE-ODE coupled system with Neumann boundary condition is considered in this paper. We design a boundary state feedback controller using the Backstepping method to stabilize the considered system. According to operator semigroup theory...
We propose a new tool to deal with autonomous ODE systems for which the solution to the Hamiltonian inverse problem is not available in the usual, classical sense. Our approach allows a class of formally conserved quantities to be constructed for dyn...
Background: This study compares system-reported organ doses (ODs) to manually calculated mean glandular doses (MGDs) in mammography across multiple centers and manufacturers in Dubai. Methods: A retrospective study of 2754 anonymized mammograms from...
This paper studies the leaderless consensus of the stochastic multi-agent systems based on partial differential equations–ordinary differential equations (PDE-ODEs). Compared with the traditional state coupling, the most significant difference...
This paper discusses consensus control of nonlinear coupled parabolic PDE-ODE-based multi-agent systems (PDE-ODEMASs). First, a consensus controller of leaderless PDE-ODEMASs is designed. Based on a Lyapunov-based approach, coupling strengths are obt...
In this article we present an ordinary differential equation based technique to study the quadratic stability of non-linear dynamical systems. The non-linear dynamical systems are modeled with norm bounded linear differential inclusions. The proposed...
In light of the planar inverse problem of Newtonian Dynamics, we study the monoparametric family of regular orbits
In this paper, the linearizability of a 2:−3 resonant system with quadratic nonlinearities is studied. We provide a list of the conditions for this family of systems having a linearizable center. The conditions for linearizablity are obtained by comp...
We study the motion of a test particle in a conservative force field. In the framework of the 2D inverse problem of Newtonian dynamics, we find 2D potentials that produce a preassigned monoparametric family of regular orbits
We study the motion of a test particle on the
Despite the huge number of studies of the three-body problem in physics and mathematics, the study of this problem remains relevant due to both its wide practical application and taking into account its fundamental importance for the theory of dynami...
In this paper, we consider nonlinear integration techniques, based on direct Padé approximation of the differential equation solution, and their application to conservative chaotic initial value problems. The properties of discrete maps obtain...
We provide a general method for identifying real quadratic polynomial dynamical systems that can be transformed to symmetric ones by a bijective polynomial map of degree one, the so-called affine map. We mainly focus on symmetry groups generated by r...
The purpose of this paper is to investigate a system of differential equations related to the viscous flow over a stretching sheet. It is assumed that the intended environment for the flow includes a chemical reaction and a magnetic field. The govern...
In this article we present and discuss a two step methodology to find the closest low rank completion of a sparse large matrix. Given a large sparse matrix M, the method consists of fixing the rank to r and then looking for the closest rank-r matrix...
The process of revitalising quiescent cells in order for them to proliferate plays a pivotal role in the repair of worn-out tissues as well as for tissue homeostasis. This process is also crucial in the growth, development and well-being of higher mu...
The timing and magnitude of the immune response (i.e., the immunodynamics) associated with the early innate immune response to viral infection display distinct trends across influenza A virus subtypes in vivo. Evidence shows that the timing of the ty...
Our paper reviews some key concepts in chemical reaction network theory and mathematical epidemiology, and examines their intersection, with three goals. The first is to make the case that mathematical epidemiology (ME), and also related sciences lik...
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