Nonlinear Analysis: Modelling and Control <p>Founded in 1997. Journal provides a multidisciplinary forum for scholars involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature.&nbsp;</p> Vilnius University Press en-US Nonlinear Analysis: Modelling and Control 1392-5113 <p>Please read the Copyright Notice in&nbsp;<a href="">Journal Policy</a>.&nbsp;</p> Eventually periodic solutions of single neuron model <p>In this paper, we consider a nonautonomous piecewise linear difference equation that describes a discrete version of a&nbsp;single neuron model with a periodic (period two and period three) internal decay rate. We investigated the periodic behavior of solutions relative to the periodic internal decay rate in our previous papers. Our goal is to prove that this model contains a large quantity of initial conditions that generate eventually periodic solutions. We will show that only periodic solutions and eventually periodic solutions exist in several cases.</p> Inese Bula Michael A. Radin Copyright (c) 2020 Inese Bula | Michael A. Radin 2020-11-01 2020-11-01 25 6 903 918 10.15388/namc.2020.25.20555 Combating unemployment through skill development <p>In this paper, we propose and analyze a nonlinear mathematical model to study the effect of skill development on unemployment. We assume that government promulgates different levels of skill development programs for unemployed persons through which two different categories of skilled persons, namely, the low-skilled and the highly-skilled persons, are coming out and the highly-skilled persons are able to create vacancies. The model is studied using stability theory of nonlinear differential equations. We find analytically that there exists a unique positive equilibrium point of the proposed model system under some conditions. Also, the resulting equilibrium is locally as well as globally stable under certain conditions. The effective use of implemented policies to control unemployment by providing skills to unemployed persons and the new vacancies created by highly-skilled persons are identified by using optimal control analysis. Finally, numerical simulation is carried out to support analytical findings.</p> Arvind Kumar Singh Pushkar Kumar Singh Arvind Kumar Misra Copyright (c) 2020 Arvind Kumar Singh | Pushkar Kumar Singh | Arvind Kumar Misra 2020-11-01 2020-11-01 25 6 919 937 10.15388/namc.2020.25.20598 Impact of social influence in English proficiency and performance in English examinations of mathematics students from a Sino-US undergraduate education program <p>This study examines the influence of certain academic and demographic variables upon the academic performance of Chinese students enrolled in a cooperative Bachelor’s degree program in Pure and Applied Mathematics. The program is English taught and jointly organised by Jiangsu University, China and Arcadia University, USA. Data from a&nbsp;sample of 166 students is processed using inferential and path analysis, as well as mathematical modelling. As evidenced by the inferential and path analysis, no steady improvement in the English proficiency of students has been observed, while the latter has been found to be influenced by gender and to strongly influence academic performance in Mathematics courses. The effects of negative social influences are assessed via a qualitative analysis of the mathematical model. Threshold quantities similar to the basic reproduction number of mathematical epidemiology have been found to be stability triggers. Possible interventional measures are discussed based on these findings.</p> Hong Zhang Wilson Osafo Apeanti Liqiong Ma Dianchen Lu Xizhong Zheng Paul Georgescu Copyright (c) 2020 Hong Zhang | Wilson Osafo Apeanti | Liqiong Ma | Dianchen Lu | Xizhong Zheng | Paul Georgescu 2020-11-01 2020-11-01 25 6 938 957 10.15388/namc.2020.25.20556 A switching control for finite-time synchronization of memristor-based BAM neural networks with stochastic disturbances <p>This paper deals with the finite-time stochastic synchronization for a class of memristorbased bidirectional associative memory neural networks (MBAMNNs) with time-varying delays and stochastic disturbances. Firstly, based on the physical property of memristor and the circuit of MBAMNNs, a MBAMNNs model with more reasonable switching conditions is established. Then, based on the theory of Filippov’s solution, by using Lyapunov–Krasovskii functionals and stochastic analysis technique, a sufficient condition is given to ensure the finite-time stochastic synchronization of MBAMNNs with a certain controller. Next, by a further discussion, an errordependent switching controller is given to shorten the stochastic settling time. Finally, numerical simulations are carried out to illustrate the effectiveness of theoretical results.</p> Liangchen Li Rui Xu Qintao Gan Jiazhe Lin Copyright (c) 2020 Liangchen Li | Rui Xu | Qintao Gan | Jiazhe Lin 2020-11-01 2020-11-01 25 6 958 979 10.15388/namc.2020.25.20557 Finite-time stochastic input-to-state stability and observer-based controller design for singular nonlinear systems <p>This paper investigated observer-based controller for a class of singular nonlinear systems with state and exogenous disturbance-dependent noise. A new sufficient condition for finite-time stochastic input-to-state stability (FTSISS) of stochastic nonlinear systems is developed. Based on the sufficient condition, a sufficient condition on impulse-free and FTSISS for corresponding closed-loop error systems is provided. A linear matrix inequality condition, which can calculate the gains of the observer and state-feedback controller, is developed. Finally, two simulation examples are employed to demonstrate the effectiveness of the proposed approaches.</p> Feng Zhao Xiangyong Chen Jinde Cao Ming Guo Jianlong Qiu Copyright (c) 2020 Feng Zhao | Xiangyong Chen | Jinde Cao | Ming Guo | Jianlong Qiu 2020-11-01 2020-11-01 25 6 980 996 10.15388/namc.2020.25.20654 Weak solvability of the unconditionally stable difference scheme for the coupled sine-Gordon system <p>In this paper, we study the existence and uniqueness of weak solution for the system of finite difference schemes for coupled sine-Gordon equations. A novel first order of accuracy unconditionally stable difference scheme is considered. The variational method also known as the energy method is applied to prove unique weak solvability.We also present a new unified numerical method for the approximate solution of this problem by combining the difference scheme and the fixed point iteration. A test problem is considered, and results of numerical experiments are presented with error analysis to verify the accuracy of the proposed numerical method.</p> Ozgur Yildirim Meltem Uzun Copyright (c) 2020 Ozgur Yildirim | Meltem Uzun 2020-11-01 2020-11-01 25 6 997 1014 10.15388/namc.2020.25.20558 Some remarks on bv(s)-metric spaces and fixed point results with an application <p>We compare the newly defined <em>b<sub>v</sub></em>(<em>s</em>)-metric spaces with several other abstract spaces like metric spaces, <em>b</em>-metric spaces and show that some well-known results, which hold in the latter class of spaces, may not hold in <em>b<sub>v</sub></em>(<em>s</em>)-metric spaces. Besides, we introduce the notions of sequential compactness and bounded compactness in the framework of <em>b<sub>v</sub></em>(<em>s</em>)-metric spaces. Using these notions, we prove some fixed point results involving Nemytzki–Edelstein type mappings in this setting, from which several comparable fixed point results can be deduced. In addition to these, we find some existence and uniqueness criteria for the solution to a certain type of mixed Fredholm–Volterra integral equations.</p> Hiranmoy Garai Lakshmi Kanta Dey Pratikshan Mondal Stojan Radenović Copyright (c) 2020 Hiranmoy Garai | Lakshmi Kanta Dey | Pratikshan Mondal | Stojan Radenović 2020-11-01 2020-11-01 25 6 1015 1034 10.15388/namc.2020.25.20559 Analysis of a model for waterborne diseases with Allee effect on bacteria <p>A limitation of current modeling studies in waterborne diseases (one of the leading causes of death worldwide) is that the intrinsic dynamics of the pathogens is poorly addressed, leading to incomplete, and often, inadequate understanding of the pathogen evolution and its impact on disease transmission and spread. To overcome these limitations, in this paper, we consider an ODEs model with bacterial growth inducing Allee effect. We adopt an adequate functional response to significantly express the shape of indirect transmission. The existence and stability of biologically meaningful equilibria is investigated through a detailed discussion of both backward and Hopf bifurcations. The sensitivity analysis of the basic reproduction number is performed. Numerical simulations confirming the obtained results in two different scenarios are shown.</p> Florinda Capone Maria Francesca Carfora Roberta De Luca Isabella Torcicollo Copyright (c) 2020 Florinda Capone | Maria Francesca Carfora | Roberta De Luca | Isabella Torcicollo 2020-11-01 2020-11-01 25 6 1035 1058 10.15388/namc.2020.25.20563 Estimation of the Hurst index of the solutions of fractional SDE with locally Lipschitz drift <p>Strongly consistent and asymptotically normal estimates of the Hurst index <em>H</em> are obtained for stochastic differential equations (SDEs) that have a unique positive solution. A strongly convergent approximation of the considered SDE solution is constructed using the backward Euler scheme. Moreover, it is proved that the Hurst estimator preserves its properties, if we replace the solution with its approximation.</p> Kęstutis Kubilius Copyright (c) 2020 Kęstutis Kubilius 2020-11-01 2020-11-01 25 6 1059 1078 10.15388/namc.2020.25.20565 Fractional integrals, derivatives and integral equations with weighted Takagi–Landsberg functions <p>In this paper, we find fractional Riemann–Liouville derivatives for the Takagi–Landsberg functions. Moreover, we introduce their generalizations called weighted Takagi–Landsberg functions, which have arbitrary bounded coefficients in the expansion under Schauder basis. The class of weighted Takagi–Landsberg functions of order <em>H</em> &gt; 0 on [0; 1] coincides with the class of <em>H</em>-Hölder continuous functions on [0; 1]. Based on computed fractional integrals and derivatives of the Haar and Schauder functions, we get a new series representation of the fractional derivatives of a Hölder continuous function. This result allows us to get a new formula of a Riemann–Stieltjes integral. The application of such series representation is a new method of numerical solution of the Volterra and linear integral equations driven by a Hölder continuous function.</p> Vitalii Makogin Yuliya Mishura Copyright (c) 2020 Vitalii Makogin | Yuliya Mishura 2020-11-01 2020-11-01 25 6 1079 1106 10.15388/namc.2020.25.20566