Nonlinear Analysis: Modelling and Control
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Fractional SDEs with stochastic forcing: Existence, uniqueness, and approximation
Full text linkIn this article, we are interested in fractional stochastic differential equations (FSDEs) with stochastic forcing, i.e., to FSDE we add a stochastic forcing term. The conditions for the existence and uniqueness of solutions of such equations are obtained, and the convergence rate of the implicit Euler approximation scheme for them is established. Such types of equations can be applied to the consideration of FSDEs with a permeable wall
Fixed points of generalized cyclic contractions without continuity and application to fractal generation
Full text linkIn this paper, we define a generalized cyclic contraction and prove a unique fixed point theorem for these contractions. An illustrative example is given, which shows that these contraction mappings may admit the discontinuities and also that an existing result in the literature is effectively generalized by the theorem. We apply the fixed point result for generation of fractal sets through construction of an iterated function system and the corresponding Hutchinsion–Barnsley operator. The above construction is illustrated by an example. The study here is in the context of metric spaces
Performance of the supervised generative classifiers of spatio-temporal areal data using various spatial autocorrelation indexes
Full text linkThis article is concerned with a generative approach to supervised classification of spatio-temporal data collected at fixed areal units and modeled by Gaussian Markov random field. We focused on the classifiers based on Bayes discriminant functions formed by the log-ratio of the class conditional likelihoods. As a novel modeling contribution, we propose to use decision threshold values induced by three popular spatial autocorrelation indexes, i.e., Moran’s I, Geary’s C and Getis–Ord G. The goal of this study is to extend the recent investigations in the context of geostatistical and hidden Markov Gaussian models to one in the context of areal Gaussian Markov models. The classifiers performance measures are chosen to be the average accuracy rate, which shows the percentage of correctly classified test data, balanced accuracy rate specified by the average of sensitivity and specificity and the geometric mean of sensitivity and specificity. The proposed methodology is illustrated using annual death rate data collected by the Institute of Hygiene of the Republic of Lithuania from the 60 unicipalities in the period from 2001 to 2019. Classification model selection procedure is illustrated on three data sets with class labels specified by the threshold to mortality index due to acute cardiovascular event, malignant neoplasms and diseases of the circulatory system. Presented critical comparison among proposed approach classifiers with various spatial autocorrelation indexes (decision threshold values) and classifier based hidden Markov model can aid in the selection of proper classification techniques for the spatio-temporal areal data
Ruin probability for renewal risk models with neutral net profit condition
Full text linkIn ruin theory, the net profit condition intuitively means that the sizes of the incurred random claims are on average less than the premiums gained between the successive interoccurrence times. The breach of the net profit condition causes guaranteed ruin in few but simple cases when both the claims’ interoccurrence time and random claims are degenerate. In this work, we give a simplified argumentation for the unavoidable ruin when the incurred claims are on average equal to the premiums gained between the successive interoccurrence times. We study the discrete-time risk model with N ∈ N periodically occurring independent distributions, the classical risk model, also known as the Cramér–Lundberg risk process, and the more general Sparre Andersen model
Optimal control results for impulsive fractional delay integrodifferential equations of order 1 < r < 2 via sectorial operator
Full text linkThis research investigates the existence of nonlocal impulsive fractional integrodifferential equations of order 1 < r < 2 with infinite delay. To begin with, we discuss the existence of a mild solution for the fractional derivatives by using the sectorial operators, the nonlinear alternative of the Leray–Schauder fixed point theorem, mixed Volterra–Fredholm integrodifferential types, and impulsive systems. Furthermore, we develop the optimal control results for the given system. The application of our findings is demonstrated with the help of an example
Event-triggered leader-following formation control of general linear multi-agent systems with distributed infinite input time delays
Full text linkBy employing event-triggered control technique, this paper investigates the leaderfollowing formation control problem of general linear multi-agent systems with distributed infinite input time delays. To decrease computing costs, a novel event-triggered formation protocol taking into consideration of the distributed infinite time delays between agents is put forward. Under the designed triggering function and triggering condition, a sufficient condition on leader-following formation is obtained, and then the Zeno-behavior of triggering time sequences is excluded for the concerned closed-loop system. The continuous update of controller for each agent is avoided. Finally, the correctness and the effectiveness of these theoretical results are demonstrated by two numerical examples
Multipoint boundary value problem for a coupled system of psi-Hilfer nonlinear implicit fractional differential equation
Full text linkThis study examines the existence and uniqueness of the solution to the coupled system of the ψ-Hilfer nonlinear implicit fractional multipoint boundary value problem. The uniqueness is shown by the Banach contraction principle, and the existence is shown by Krasnosel’skii’s fixed point theorem in a special working space. An example is presented to verify our results. The existence and uniqueness of the solution are analysed graphically
Bifurcation analysis and optimal control of a network-based SIR model with the impact of medical resources
Full text linkA new network-based SIR epidemic model, which incorporates the individual medical resource factor and public medical resource factor is proposed. It is verified that the larger the public medical resource factor, the smaller the control reproduction number, and the larger individual medical resource factor can weaken the spread of diseases. We found that the control reproduction number below unity is not enough to ensure global asymptotic stability of the disease-free equilibrium. When the number of hospital beds or the individual medical resource factor is small enough, the system will undergoes backward bifurcation. Moreover, the existence and uniqueness of the optimal control and two time-varying variables’s optimal solutions are obtained. On the scale-free network, the level of optimal control is also proved to be different for different degrees. Finally, the theoretical results are illustrated by numerical simulations. This study suggests that maintaining sufficient both public medical resources and individual medical resources is crucial for the control of infectious diseases
Modelling asthma development in a population with genetic risk and polluted environment
Full text linkEnvironmental pollutant continues to pose a great threat to public health, leading to development of chronic diseases. In this study, a nonlinear mathematical model is formulated and analysed to study the effect of genetic risk, environmental pollutant, public health education/awareness on asthma development. Conditions for the existence of the unique positive steady state and permanence of the system are assessed. Using Lyapunov function analysis, the unique positive steady state is locally and globally asymptotically stable. Results reveal that genetic risk, pollutant emission rate, effective exposure rate of population to polluted environment and recurrence rate contribute to asthma prevalence. However, sufficiently effective pollutant reduction strategies, improvement in compliance to public health education/awareness together with human dependent environmental pollutant depletion lead to a marked reduction in disease prevalence
Spatiotemporal dynamics in a toxin-producing predator–prey model with threshold harvesting
Full text linkIn this paper, we propose a toxin-producing predator–prey model with threshold harvesting and study spatiotemporal dynamics of the model under the homogeneous Neumann boundary conditions. At first, the persistence property of solutions to the system is investigated. Then the explicit requirements for the existence of nonconstant steady state solutions are derived by studying the relevant characteristic equation. These steady states occur from related constant steady states via steady state bifurcation. Throughout the analysis of the amplitude equations of Turing pattern by the multiple scale method, pattern formation can be found. Finally, we display umerical simulations to verify the theoretical outcomes