Practical stability for fractional impulsive control systems with noninstantaneous impulses on networks

This paper investigates practical stability for a class of fractional-order impulsive control coupled systems with noninstantaneous impulses on networks. Using graph theory and Lyapunov method, new criteria for practical stability, uniform practical stability as well as practical asymptotic stability are established. In this paper, we extend graph theory to fractional-order system via piecewise Lyapunov-like functions in each vertex system to construct global Lyapunov-like functions. Our results are generalization of some known results of practical stability in the literature and provide a new method of impulsive control law for impulsive control systems with noninstantaneous impulses. Examples are given to illustrate the effectiveness of our results

The hunting cooperation of a predator under two prey's competition and fear-effect in the prey-predator fractional-order model

<abstract><p>This paper investigates a fractional-order mathematical model of predator-prey interaction in the ecology considering the fear of the prey, which is generated in addition by competition of two prey species, to the predator that is in cooperation with its species to hunt the preys. At first, we show that the system has non-negative solutions. The existence and uniqueness of the established fractional-order differential equation system were proven using the Lipschitz Criteria. In applying the theory of Routh-Hurwitz Criteria, we determine the stability of the equilibria based on specific conditions. The discretization of the fractional-order system provides us information to show that the system undergoes Neimark-Sacker Bifurcation. In the end, a series of numerical simulations are conducted to verify the theoretical part of the study and authenticate the effect of fear and fractional order on our model's behavior.</p></abstract>

Superconvergent interpolants for Gaussian collocation solutions of mixed order BVODE systems

<abstract><p>The high quality COLSYS/COLNEW collocation software package is widely used for the numerical solution of boundary value ODEs (BVODEs), often through interfaces to computing environments such as Scilab, R, and Python. The continuous collocation solution returned by the code is much more accurate at a set of mesh points that partition the problem domain than it is elsewhere; the mesh point values are said to be superconvergent. In order to improve the accuracy of the continuous solution approximation at non-mesh points, when the BVODE is expressed in first order system form, an approach based on continuous Runge-Kutta (CRK) methods has been used to obtain a superconvergent interpolant (SCI) across the problem domain. Based on this approach, recent work has seen the development of a new, more efficient version of COLSYS/COLNEW that returns an error controlled SCI.</p> <p>However, most systems of BVODEs include higher derivatives and a feature of COLSYS/COLNEW is that it can directly treat such mixed order BVODE systems, resulting in improved efficiency, continuity of the approximate solution, and user convenience. In this paper we generalize the approach mentioned above for first order systems to obtain SCIs for collocation solutions of mixed order BVODE systems. The main contribution of this paper is the derivation of generalizations of continuous Runge-Kutta-Nyström methods that form the basis for SCIs for this more general problem class. We provide numerical results that (ⅰ) show that the SCIs are much more accurate than the collocation solutions at non-mesh points, (ⅱ) verify the order of accuracy of these SCIs, and (ⅲ) show that the cost of utilizing the SCIs is a small fraction of the cost of computing the collocation solution upon which they are based.</p></abstract>

Optimized operation of regional reserve forces in a changing future security environment

The Republic of Korea Reserve Forces (ROKRF), established in 1968, continue to function through continuous changes such as improving laws and systems and optimizing organizations while complying with social and policy changes. However, the reduction of standing forces, changes in the operating environment, and the reduction of reserve forces required to carry out operations require the re-establishment of the concept of operation of regional reserve forces. In this study, we aimed to diagnose the phenomenon of regional reserve groups and derive an optimized operation plan for regional reserve groups in consideration of changes in the future security environment, operation support system, and law and order system. The operating system presented the mission of establishing local reserve forces suitable for the operating environment, organization, and organization maintenance for the future as well as maintenance and development of combat power through education and training. Finally, in the law and order system section, a plan to revise laws was proposed in consideration of the task of operating and constructing regional reserve forces and re-establishing them.

New Optical Soliton Solutions for Coupled Resonant Davey-Stewartson System with Conformable Operator

This paper investigates the novel soliton solutions of the coupled fractional system of the resonant Davey-Stewartson equations. The fractional derivatives are considered in terms of conformable sense. Accordingly, we utilize a complex traveling wave transformation to reduce the proposed system to an integer-order system of ordinary differential equations. The phase portrait and the equilibria of the obtained integer-order ordinary differential system will be studied. Using suitable mathematical assumptions, the new types of bright, singular, and dark soliton solutions are derived and established in view of the hyperbolic, trigonometric, and rational functions of the governing system. To achieve this, illustrative examples of the fractional Davey-Stewartson system are provided to demonstrate the feasibility and reliability of the procedure used in this study. The trajectory solutions of the traveling waves are shown explicitly and graphically. The effect of conformable derivatives on behavior of acquired solutions for different fractional orders is also discussed. By comparing the proposed method with the other existing methods, the results show that the execute of this method is concise, simple, and straightforward. The results are useful for obtaining and explaining some new soliton phenomena.

Impact of media coverage on a fractional-order SIR epidemic model

In this work, we formulated and analyzed a fractional-order epidemic model of infectious disease (such as SARS, 2019-nCoV and COVID-19) concerning media effect. The model is based on classical susceptible-infected-recovered (SIR) model. Basic properties regarding positivity, boundedness and non-negative solutions are discussed. Basic reproduction number [Formula: see text] of the system has been calculated using next-generation matrix method and it is seen that the disease-free equilibrium is locally as well as globally asymptotically stable if [Formula: see text], otherwise unstable. The existence of endemic equilibrium point is established using the Lambert W function. The condition for global stability has been derived. Numerical simulation suggests that fractional order and media have a large effect on our system dynamics. When media impact is stronger enough, our fractional-order system stabilizes the oscillation.

Sliding Mode Analysis of a Counterbalance Valve Induced Instability in an Electrohydraulic Drive

This paper analyzes dynamic effects of an electro-hydraulic drive which uses a counter-balance valve for rod volume compensation. It shows that local stability analysis is not sufficient in this particular case to get general statements of the system's chattering properties. A reduced-order switched system is proposed to gain deeper insights in system dynamics with saturation effects such as the end-stop of a valve poppet and solutions are compared numerically to the full-system dynamics which incorporates pressure built-up, piston and valve dynamics as well as motor dynamics. It is shown that in cases of e.g. fast valves with small cracking pressures undesirable chattering of the full system exists which can be easily understood in terms of the reduced-order system in form of sliding mode solutions. The paper also describes under which conditions such sliding modes exist, how they behave and how they can be interpreted in terms of the full system.

Design, Analysis and Comparison of a Nonstandard Computational Method for the Solution of a General Stochastic Fractional Epidemic Model

Malaria is a deadly human disease that is still a major cause of casualties worldwide. In this work, we consider the fractional-order system of malaria pestilence. Further, the essential traits of the model are investigated carefully. To this end, the stability of the model at equilibrium points is investigated by applying the Jacobian matrix technique. The contribution of the basic reproduction number, R0, in the infection dynamics and stability analysis is elucidated. The results indicate that the given system is locally asymptotically stable at the disease-free steady-state solution when R0<1. A similar result is obtained for the endemic equilibrium when R0>1. The underlying system shows global stability at both steady states. The fractional-order system is converted into a stochastic model. For a more realistic study of the disease dynamics, the non-parametric perturbation version of the stochastic epidemic model is developed and studied numerically. The general stochastic fractional Euler method, Runge–Kutta method, and a proposed numerical method are applied to solve the model. The standard techniques fail to preserve the positivity property of the continuous system. Meanwhile, the proposed stochastic fractional nonstandard finite-difference method preserves the positivity. For the boundedness of the nonstandard finite-difference scheme, a result is established. All the analytical results are verified by numerical simulations. A comparison of the numerical techniques is carried out graphically. The conclusions of the study are discussed as a closing note.