Differential System Research Articles

Importance of Activation Energy on Magnetized Dissipative Casson-Maxwell Fluid through Porous Medium Incorporating Chemical Reaction, Joule Heating, and Soret Effects: Numerical Study

In recent decades, the study of non-Newtonian fluids has attracted the interest of numerous researchers. Their study is encouraged by the significance of these fluids in fields including industrial implementations. Furthermore, the importance of heat and mass transfer is greatly increased by a variety of scientific and engineering processes, including air conditioning, crop damage, refrigeration, equipment power collectors, and heat exchangers. The key objective of this work is to use the mathematical representation of a chemically reactive Casson-Maxwell fluid over a stretched sheet circumstance. Arrhenius activation energy and aspects of the magnetic field also have a role. In addition, the consequences of both viscous dissipation, Joule heating, and nonlinear thermal radiation are considered. The method transforms partial differential equations originating in fluidic systems into nonlinear differential equation systems with the proper degree of similarity which is subsequently resolved utilizing the Lobatto IIIA technique’s powerful computing capabilities. It is important to recall that the velocity profile drops as the Maxwell fluid parameter increases. Additionally, the increase in the temperature ratio parameter raises both the fluid’s temperature and the corresponding thickness of the boundary layer.

On Some Aspects of the Courant-Type Algebroids, the Related Coadjoint Orbits and Integrable Systems

Poisson structures related to affine Courant-type algebroids are analyzed, including those related with cotangent bundles on Lie-group manifolds. Special attention is paid to Courant-type algebroids and their related R structures generated by suitably defined tensor mappings. Lie–Poisson brackets that are invariant with respect to the coadjoint action of the loop diffeomorphism group are created, and the related Courant-type algebroids are described. The corresponding integrable Hamiltonian flows generated by Casimir functionals and generalizing so-called heavenly-type differential systems describing diverse geometric structures of conformal type in finite dimensional Riemannian manifolds are described.

Race specific and non-specific resistance to Magnaporthe oryzae and QTL mapping in wild introgression lines using the standard differential system

Race specific and non-specific resistance to Magnaporthe oryzae and QTL mapping in wild introgression lines using the standard differential system

A Study on Approximate Controllability of Ψ-Caputo Fractional Differential Equations with Impulsive Effects

In this article, we studied the approximate controllability of Ψ-Caputo fractional differential systems. We prove the sufficient conditions for an abstract Cauchy problem invloving infinite delay, impulsive and nonlocal conditions. The result is shown by means of the infinitesimal operator, semigroup theory, fractional calculus, and Schauder’s fixed point theorem. First, we prove the existence of the mild solution and demonstrate that the Ψ-Caputo fractional system is approximately controllable. Finally, an example is given to analyse the obtained results.

Error analysis of a highly efficient and accurate temporal multiscale method for a fractional differential system

This work is concerned with a nonlinear coupled system of fractional ordinary differential equations (FODEs) with multiple scales in time. The micro system is a nonlinear differential equation with a periodic applied force and the macro system is a fractional differential equation. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the solution of the coupled fractional problem at a lower computational cost, which calls for us to develop an effective analysis and computation framework. We derive a periodic auxiliary system to approximate the original system and give error estimates. Then we propose a numerical scheme based on the auxiliary problem and analyze the discrete error. An efficient multiscale algorithm that is also applicable to 2-D and 3-D problems is designed. The results of numerical experiments demonstrate the accuracy and computational efficiency of the proposed multiscale method. It is observed that, the computational time is significantly reduced and the multiscale method performs very well in comparison to the fully resolved simulation. Furthermore, as a particular example of applications, we consider a simplified model of the atherosclerotic plaque growth problem, and simply evaluate the effect of fractional parameter and damping coefficient on plaque growth and discuss the physical implication.

Dynamics of the Isotropic Star Differential System from the Mathematical and Physical Point of Views

The following differential quadratic polynomial differential system dxdt=y−x, dydt=2y−yγ−12−γy−5γ−4γ−1x, when the parameter γ∈(1,2] models the structure equations of an isotropic star having a linear barotropic equation of state, being x=m(r)/r where m(r)≥0 is the mass inside the sphere of radius r of the star, y=4πr2ρ where ρ is the density of the star, and t=ln(r/R) where R is the radius of the star. First, we classify all the topologically non-equivalent phase portraits in the Poincaré disc of these quadratic polynomial differential systems for all values of the parameter γ∈R∖{1}. Second, using the information of the different phase portraits obtained we classify the possible limit values of m(r)/r and 4πr2ρ of an isotropic star when r decreases.

RDmaster: A novel phenotype-oriented dialogue system supporting differential diagnosis of rare disease

BackgroundClinicians often lack the necessary expertise to differentially diagnose multiple underlying rare diseases (RDs) due to their complex and overlapping clinical features, leading to misdiagnoses and delayed treatments. The aim of this study is to develop a novel electronic differential diagnostic support system for RDs. MethodThrough integrating two Bayesian diagnostic methods, a candidate list was generated with enhance clinical interpretability for the further Q&A based differential diagnosis (DDX). To achieve an efficient Q&A dialogue strategy, we introduce a novel metric named the adaptive information gain and Gini index (AIGGI) to evaluate the expected gain of interrogated phenotypes within real-time diagnostic states. ResultsThis DDX tool called RDmaster has been implemented as a web-based platform (http://rdmaster.nbscn.org/). A diagnostic trial involving 238 published RD patients revealed that RDmaster outperformed existing RD diagnostic tools, as well as ChatGPT, and was shown to enhance the diagnostic accuracy through its Q&A system. ConclusionsThe RDmaster offers an effective multi-omics differential diagnostic technique and outperforms existing tools and popular large language models, particularly enhancing differential diagnosis in collecting diagnostically beneficial phenotypes.

Dynamics of a random Hopfield neural lattice model with adaptive synapses and delayed Hebbian learning

UDC 517.9 A Dong–Hopfield neural lattice model with random external forcing and delayed response to the evolution of interconnection weights is developed and studied. The interconnection weights evolve according to the Hebbian learning rule with a decay term and contribute to changes in the states after a short delay. The lattice system is first reformulated as a coupled functional-ordinary differential equation system on an appropriate product space. Then the solution of the system is shown to exist and be unique. Furthermore it is shown that the system of equations generates a continuous random dynamical system. Finally, the existence of random attractors for the random dynamical system generated by the Dong–Hopfield model is established.

Limit Cycles of Discontinuous Piecewise Differential Systems Formed by Linear and Cubic Centers via Averaging Theory

Limit Cycles of Discontinuous Piecewise Differential Systems Formed by Linear and Cubic Centers via Averaging Theory

Exponential stability of impulsive delayed nonlinear hybrid differential systems

Exponential stability of impulsive delayed nonlinear hybrid differential systems

Exact solution of the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model

An exact solution of an initial value problem for the Susceptible–Exposed–Infectious–Recovered–Deceased (SEIRD) epidemic model is derived, and various properties of the exact solution are obtained. It is shown that the parametric form of the exact solution satisfies some linear differential system including a positive solution of an Abel differential equation of the second kind. In this paper Abel differential equations play an important role in establishing the exact solution of the SEIRD differential system, in particular the number of infected individuals can be represented in a simple form by using a positive solution of an initial value problem for an Abel differential equation. Uniqueness of positive solutions of an initial value problem to SEIRD differential system is also investigated, and it is shown that the exact solution is a unique solution in the class of positive solutions.

Limit cycles of a generalised Mathieu differential system

Abstract We study the maximum number of limit cycles which bifurcate from the periodic orbits of the linear centre ̇x = y, ̇y = −x, when it is perturbed in the form x ˙ = y - ɛ ( 1 + cos l θ ) P ( x , y ) , y ˙ = - x - ɛ ( 1 + cos m θ ) Q ( x , y ) , \dot x = y - \varepsilon \left( {1 + {{\cos }^l}\theta } \right)P\left( {x,y} \right),\,\,\,\,\dot y = - x - \varepsilon \left( {1 + {{\cos }^m}\theta } \right)Q\left( {x,y} \right), where ε > 0 is a small parameter, l and m are positive integers, P(x, y) and Q(x, y) are arbitrary polynomials of degree n, and θ = arctan(y/x). As we shall see the differential system (1) is a generalisation of the Mathieu differential equation. The tool for studying such limit cycles is the averaging theory.

A Gudermannian neural network performance for the numerical environmental and economic model

The present work is to exploit the Gudermannian neural network (GNN) using the global competency of genetic algorithm (GA) and quick local refinements of sequential quadratic programming approach (SQPA), i.e., GNN-GA-SQPA for the nonlinear economic and environmental system. The differential form of the nonlinear system depends upon three classes, system capability of industrial elements, implementation cost of control values and a new diagnostics technical elimination cost. An error-based fitness function is constructed using the differential system and then optimized by using the hybrid competency of the GA-SQPA. Ten numbers of neurons, a merit Gudermannian function, and the suitable weight vectors are presented in the neural network construction. The accuracy of the GNN-GA-SQPA is assessed through the comparisons and the negligible performances of absolute error. The statistical observations using single and multiple trials validate the stability of the scheme.

The μ-neutral fractional multi-delayed differential equations

The μ-neutral linear fractional multi-delayed differential nonhomogeneous system with noncommutative coefficient matrices is introduced. The novel μ-neutral multi-delayed perturbation of Mittag-Leffler type matrix function is proposed. Based on this, an explicit solution to the system is investigated step by step. The existence uniqueness of solutions to μ-neutral nonlinear fractional multi-delayed differential system is obtained with regard to the supremum norm. The notion of stability analysis in the sense of solutions to the described system is discussed on the grounds of the fixed point approach.

A Differential Brake-Actuated Steering System for Redundancy of Steer-by-Wire

A Differential Brake-Actuated Steering System for Redundancy of Steer-by-Wire

Hydrodynamic Model for Particle Beam-Driven Wakefield in Carbon Nanotubes

The charged particles moving through a carbon nanotube (CNT) may be used to excite electromagnetic modes in the electron gas produced in the cylindrical graphene shell that makes up a nanotube wall. This effect has recently been proposed as a potential novel method of short-wavelength-high-gradient particle acceleration. In this contribution, the existing theory based on a linearized hydrodynamic model for a localized point-charge propagating in a single wall nanotube (SWNT) is reviewed. In this model, the electron gas is treated as a plasma with additional contributions to the fluid momentum equation from specific solid-state properties of the gas. The governing set of differential equations is formed by the continuity and momentum equations for the involved species. These equations are then coupled by Maxwell’s equations. The differential equation system is solved applying a modified Fourier-Bessel transform. An analysis has been realized to determine the plasma modes able to excite a longitudinal electrical wakefield component in the SWNT to accelerate test charges. Numerical results are obtained showing the influence of the damping factor, the velocity of the driver, the nanotube radius, and the particle position on the excited wakefields. A discussion is presented on the suitability and possible limitations of using this method for modelling CNT-based particle acceleration.

Evolutionary Dynamics Optimal Research-Oriented Tumor Immunity Architecture.

The article is devoted to evolutionary dynamics optimal control-oriented tumor immune differential game system. First, the mathematical model covering immune cells and tumor cells considering the effects of chemotherapy drugs and immune agents. Second, the bounded optimal control problem covering is transformed into solving Hamilton-Jacobi-Bellman (HJB) equation considering the actual constraints and infinite-horizon performance index based on minimizing the amount of medication administered. Finally, approximate optimal control strategy is acquired through iterative-dual heuristic dynamic programming (I-DHP) algorithm avoiding dimensional disaster effectively and providing optimal treatment scheme for clinical applications.

A class of evolution differential inclusion systems

The main purpose of this paper is to study an abstract system which consists of a non-linear differential inclusion with $C_0$-semigroups and history-dependent operators combined with an evolutionary non-linear inclusion involving pseudomonotone operators, which contains several interesting problems as special cases. We first introduce a hybrid iterative system by using the Rothe method, pseudomonotone operators theory, and a feedback iterative technique. Then, the existence and a priori estimates for solutions to a series of approximating discrete problems are established. Furthermore, through a limiting procedure for solutions of the hybrid iterative system, we show that the existence of solutions to the original problem.

Design and Analysis of High Data Rate Four-Dimensional Index Modulation for Differential Chaos Shift Keying System

Design and Analysis of High Data Rate Four-Dimensional Index Modulation for Differential Chaos Shift Keying System

A class of evolution differential inclusion systems

The main purpose of this paper is to study an abstract system which consists of a non-linear differential inclusion with $C_0$-semigroups and history-dependent operators combined with an evolutionary non-linear inclusion involving pseudomonotone operators, which contains several interesting problems as special cases. We first introduce a hybrid iterative system by using the Rothe method, pseudomonotone operators theory, and a feedback iterative technique. Then, the existence and a priori estimates for solutions to a series of approximating discrete problems are established. Furthermore, through a limiting procedure for solutions of the hybrid iterative system, we show that the existence of solutions to the original problem.