Hybrid System Of Differential Equations Research Articles

Задача управления мультиагентной транспортной системой

A new class of control problems for a certain transport system is considered. The peculiarity of the system is the variable number of participants in the control process. The regrouping of participants, along with their unification and dispersal, is determined by the specified target points of visit, the initial point of departure and the final point of completion of the system’s movement, and the constructed trajectories. The structure of a multi-agent transport system implies the presence of primary and secondary carriers, with the former being able to transport the latter at some stages. It is at such moments that the number of participants in the control process changes. In the constructed mathematical model of the movements of the system under consideration and its control, a hybrid system of differential equations with switching is obtained, containing continuous and discrete components. The problem of finding optimal routes under certain constraints is solved.

Existence of solutions for coupled hybrid systems of differential equations for microscopic dynamics and local concentrations

Existence of solutions for coupled hybrid systems of differential equations for microscopic dynamics and local concentrations

Existence of solutions for hybrid systems of differential equations under exogenous information with discontinuous source term

In the mathematical modeling framework, the adoption of multiscale approaches provides a better alternative to the well-known individual-based and continuum ones. From a mathematical point of view, the emerging class of systems is characterized by the coupling of ordinary and partial differential equations. Generalizing the hybrid structure of models of the literature, we prove the existence of a weak solution for the case in which discontinuous functions model the source term of the parabolic equation, and we provide also some regularity properties.

A fractional‐order hybrid system of differential equations: Existence theory and numerical solutions

This paper is a study about a fractional‐order hybrid system of two fractional‐order differential equations. We have given the existence of solution and uniqueness of solutions, and finally, the numerical solutions for an application is presented. The existence results are based on the classical fixed‐point approach while the numerical results are obtained with the help of fractional‐order Euler's technique. In the numerical solutions, we can see that the orders of the differential equations are playing important role. We have given related literature for the readers for their detail explanation.

Theoretical Foundations of the Study of a Certain Class of Hybrid Systems of Differential Equations

In this paper, we consider boundary-value problems for a new class of hybrid systems of differential equations whose coefficients contain the Dirac delta-function. Hybrid systems are systems that contain both ordinary and partial differential equations; such systems appear, for example, when equations of motion of mechanical systems of rigid bodies attached to a beam by elastic bonds are derived from the Hamilton–Ostrogradsky variational principle. We present examples that lead to such systems and introduce the notions of generalized solutions and eigenvalues of a boundary-value problem. We also compare results of numerical simulations based on methods proposed in this paper with results obtained by previously known methods and show that our approach is reliable and universal.

An equilibrium position in the generalized mathematical model of a system of rigid bodies elastically mounted on an Euler-Bernoulli beam

The paper considers a generalized mathematical model of a class of mechanical systems, which represent systems of rigid bodies elastically mounted on an Euler-Bernoulli beam. This model has the form of a hybrid system of differential equations having a definite structure and describing the process of transfer (transition) of the system within the frames of some coordinated system chosen. On the basis of the generalized mathematical model, a generalized approach to finding the equilibrium position for mechanical systems, which belong to a given class of systems, in a chosen coordinate system has been proposed. The equilibrium position of a mechanical system is understood as the solution of a definite hybrid system of differential equations, furthermore, this solution does not change with time. The equilibrium position of a mechanical system within a given coordinate system allows one to proceed - by replacement of the variables - to consideration of the generalized mathematical model studied earlier and describing transfer of a system with respect to the equilibrium.

Global dynamics for a model of amyloid fibril formation in pancreatic islet beta cells subjected to a therapy

Amyloid polypeptide (IAPP) fibril formation is the main cause of type II diabetes mellitus (T2DM) disease and cardiovascular disease (CVD). Therefore, implementing therapeutic interventions strategies to control IAPP fibril formation plays a crucial role in preventing and managing T2DM disease and CVD. For this purpose, in this paper, we make use of a mathematical model to investigate the effects of drug therapy on the dynamics of amyloid fibril formation (or amyloid plaques). The model is a hybrid system of differential equations consisting of ODEs and (hyperbolic) PDE. The (global) stability analysis is established through the construction of suitable Lyapunov functionals and application of Lasalle's invariance principle. Moreover, stability of the disease steady state is fully determined by a threshold condition, which is based on the total population of IAPP polymers.

Global solutions for a path-dependent hybrid system of differential equations under parabolic signal

In this paper we propose local and global existence results for the solution of systems characterized by the coupling of ODEs and PDEs. The coexistence of distinct mathematical formalisms represents the main feature of hybrid approaches, in which the dynamics of interacting agents are driven by second-order ODEs, while reaction–diffusion equations are used to model the time evolution of a signal influencing them. We first present an existence result of the solution, locally in time. In particular, we generalize the framework of recent works, presented in the literature with a modeling and numerical approach, which have not been investigated from an analytical point of view so far. Then, the previous result is extended in order to obtain a global solution.

A generalized mathematical model for a class of mechanical systems with lumped and distributed parameters

A hybrid system of differential equations, which represents a generalized mathematical model for a system of rigid bodies mounted on an Euler-Bernoulli beam with the aid of springs, is described in the general form. A hybrid system of differential equations is understood as a system of differential equations composed of ordinary differential equations and partial differential equations. Hybrid systems of differential equations of such type are normally constructed in the process of inference of dynamic equations for a given class of mechanical systems with the use of the Hamiltonian variation principle. The paper considers the analytical-numerical method proposed by the author, which is based on the mathematical apparatus of generalized functions. The comparative analysis of results of numerical computations obtained by the authoros method to the computational results obtained by the techniques known from the literature has shown the plausibility and universality of the authoros approach.

Equations of Motion of a Rigid Body with Two Elastic Rods

In the paper we propose a mathematical model of a mechanical system consisting of a rigid body and two rigidly connected elastic straight rods located in the same plane. The system rotates around the axis passing through the mass center of a rigid body and perpendicular to the plane of the rods. The rods are modeled by the Euler–Bernoulli beam. The mathematical model is an initial-boundary value problem for a hybrid system of differential equations. The cases of fast and slow rotations of the system are considered.

A Generalized Solution of an Initial Boundary Value Problem Arising in the Mechanics of Discrete-Continuous Systems

In this paper we define a generalized solution of an initial boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We have proved the existence theorem for a generalized solution, its uniqueness, the correctness of the problem. An analytical formula for the solution is found. Such a system of differential equations arises in the study of discrete-continuum mechanical systems.

Solutions Stability of Initial Boundary Problem, Modeling of Dynamics of Some Discrete Continuum Mechanical System

The solution stability of an initial boundary problem for a linear hybrid system of differential equations, which models the rotation of a rigid body with two elastic rods located in the same plane is studied in the paper. To an axis passing through the mass center of the rigid body perpendicularly to the rods location plane is applied the stabilizing moment proportional to the angle of the system rotation, derivative of the angle, integral of the angle. The external moment provides a feedback. A method of studying the behavior of solutions of the initial boundary problem is proposed. This method allows to exclude from the hybrid system of differential equations partial differential equations, which describe the dynamics of distributed elements of a mechanical system. It allows us to build one equation for an angle of the system rotation. Its characteristic equation defines the stability of solutions of all the system. In the space of feedback-coefficients the areas that provide the asymptotic stability of solutions of the initial boundary problem are built up.

Motion equations of a rigid body with two elastic rods

A mathematical model of a mechanical system consisting of a rigid body and two rigidly connected elastic straight rods located in the same plane is offered in this paper. The system rotates around the axis passing through the mass center of a rigid body and perpendicular to the plane of the rods. The rods are modeled by the Euler-Bernoulli beam. The mathematical model is an initialboundary value problem for a hybrid system of differential equations. The cases of fast and slow rotations of the system are considered.

A generalized solution of an initial-boundary value problem arising in the mechanics of discrete-continuous systems

We define a generalized solution of an initial-boundary value problem for a linear system of differential equations with one ordinary differential equation and two partial differential equations (a hybrid system of differential equations). We prove that the problem is well-posed and has a unique generalized solution. An analytical formula for the solution is found. Such systems of differential equations arise in studying discrete-continuum mechanical systems.

Yeast Network and Report of New Stochastic-Credibility Cell Cycle Models

A cell division cycle is a set of events that take place in a cell, characterized by a period of cell growing and cell duplication, these processes taking place in five phases. Many genes and proteins regulate cell division. There are presented mechanisms that stop and restart cell divisions for budding yeast, by considering stochastic noise (extrinsic noise). Fuzzy phenomenon was introduced by Li and Liu and it is based on credibility measure. A Wiener-Liu process (hybrid process) is a mixture of randomness and fuzziness. We consider the study of a generic cell cycle model for budding yeast, representing a complex network of interactions between genes and proteins. In this sense, the present work has two parts: first we give a short review the state-of-art in yeast gene interaction networks studies, and next we report our own results. We study this model by considering stochastic approach (by writing stochastic system of differential equations), fuzzy approach (the fuzzy system of differential equations associated to the deterministic system) and hybrid system of differential equations, as a combination of randomness and fuzziness.

Observations on the Steady-State Solution of an Extremely Flexible Spinning Disk With a Transverse Load

The steady deflection of a transversely loaded, extremely flexible, spinning disk is studied. Membrane theory is used to predict the shapes and locations of waves that dominate the response. It is found that waves in disconnected regions are possible. Some results are presented to show how disk stiffness moderates the membrane waves, the most important result being an upper bound on the highest ordered wave of significant amplitude. A hybrid system of differential equations and boundary conditions is developed to replace the pure membrane formulation that is singular, and the full fourth-order plate formulation that is numerically sensitive. The hybrid formulation retains the salient features of the flexible disk response and facilitates calculations for very small disk stiffnesses.