Nonlinear Analysis: Modelling and Control https://www.journals.vu.lt/nonlinear-analysis <p>Founded in 1997 and dedicated to publishing interdisciplinary works on nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. Indexed in the <em>Scopus</em> (Q2) database since 2009 and in the<em> Web of Science</em> (Q1) database since 2010.</p> Vilnius University Press en-US Nonlinear Analysis: Modelling and Control 1392-5113 <p>Please read the Copyright Notice in&nbsp;<a href="http://www.zurnalai.vu.lt/acta-paedagogica-vilnensia/journalpolicy">Journal Policy</a>.&nbsp;</p> Finite-time stabilization of discontinuous fuzzy inertial Cohen–Grossberg neural networks with mixed time-varying delays https://www.journals.vu.lt/nonlinear-analysis/article/view/23935 <p>This article aims to study a class of discontinuous fuzzy inertial Cohen–Grossberg neural networks (DFICGNNs) with discrete and distributed time-delays. First of all, in order to deal with the discontinuities by the differential inclusion theory, based on a generalized variable transformation including two tunable variables, the mixed time-varying delayed DFICGNN is transformed into a first-order differential system. Then, by constructing a modified Lyapunov–Krasovskii functional concerning with the mixed time-varying delays and designing a delayed feedback control law, delay-dependent criteria formulated by algebraic inequalities are derived for guaranteeing the finite-time stabilization (FTS) for the addressed system. Moreover, the settling time is estimated. Some related stability results on inertial neural networks is extended. Finally, two numerical examples are carried out to verify the effectiveness of the established results.</p> Fanchao Kong Quanxin Zhu Rathinasamy Sakthivel Copyright (c) 2021 Fanchao Kong | Quanxin Zhu | Rathinasamy Sakthivel https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 759 780 10.15388/namc.2021.26.23935 A study of common fixed points that belong to zeros of a certain given function with applications https://www.journals.vu.lt/nonlinear-analysis/article/view/21945 <p>In this paper, we establish some point of <em>φ</em>-coincidence and common <em>φ</em>-fixed point results for two self-mappings defined on a metric space via extended <em>C<sub>G</sub></em>-simulation functions. By giving an example we show that the obtained results are a proper extension of several well-known results in the existing literature. As applications of our results, we deduce some results in partial metric spaces besides proving an existence and uniqueness result on the solution of system of integral equations.</p> Hayel N. Saleh Mohammad Imdad Erdal Karapinar Copyright (c) 2021 Hayel N. Saleh | Mohammad Imdad | Erdal Karapinar https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 781 800 10.15388/namc.2021.26.21945 Finite-time ruin probability of a perturbed risk model with dependent main and delayed claims https://www.journals.vu.lt/nonlinear-analysis/article/view/23963 <p>This paper considers a delayed claim risk model with stochastic return and Brownian perturbation in which each main claim may be accompanied with a delayed claim occurring after a stochastic period of time, and the price process of the investment portfolio is described as a geometric Lévy process. By means of the asymptotic results for randomly weighted sum of dependent subexponential random variables we obtain some asymptotics for finite-time ruin probability. A simulation study is also performed to check the accuracy of the obtained theoretical result via the crude Monte Carlo method.</p> Yang Yang Xinzhi Wang Zhimin Zhang Copyright (c) 2021 Yang Yang | Xinzhi Wang | Zhimin Zhang https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 801 820 10.15388/namc.2021.26.23963 On the new Hyers–Ulam–Rassias stability of the generalized cubic set-valued mapping in the incomplete normed spaces https://www.journals.vu.lt/nonlinear-analysis/article/view/24367 <p>We present a novel generalization of the Hyers–Ulam–Rassias stability definition to study a generalized cubic set-valued mapping in normed spaces. In order to achieve our goals, we have applied a brand new fixed point alternative. Meanwhile, we have obtained a practicable example demonstrating the stability of a cubic mapping that is not defined as stable according to the previously applied methods and procedures.</p> Maryam Ramezani Hamid Baghani Juan J. Nieto Copyright (c) 2021 Maryam Ramezani | Hamid Baghani | Juan J. Nieto https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 821 841 10.15388/namc.2021.26.24367 A mathematical view towards improving undergraduate student performance and mitigating dropout risks https://www.journals.vu.lt/nonlinear-analysis/article/view/24120 <p>In this paper, we assess the relevance of social and cognitive factors such as self-efficacy, locus of control and exposure to negative social influence in relation to undergraduate student dropout. To this purpose, we analyze a compartmental model involving a system of nonlinear ODEs, which is loosely based upon the SIR model of mathematical epidemiology and describes the academic performance of the student population. We examine threshold values that govern the stability of the equilibria and can be viewed as target values to be reached in order to alleviate undergraduate students dropout. A backward bifurcation is observed to occur, analytically and numerically, provided that certain conditions are satisfied.</p> <p><br>A sensitivity analysis is then performed to find how the threshold values respond to changes in the parameters, a procedure for estimating these parameters being also proposed. Concrete values are then computed using survey data from a Ghanaian university. The impact of parameter variation upon the dynamics of the system, particularly on certain population sizes and on threshold values, is also numerically illustrated. Our findings are then interpreted from a social cognitive perspective, realistic policy changes being proposed along with appropriate teaching and coaching strategies.</p> Hong Zhang Wilson Osafo Apeanti Saviour Worlanyo Akuamoah David Yaro Paul Georgescu Copyright (c) 2021 Hong Zhang | Wilson Osafo Apeanti | Saviour Worlanyo Akuamoah | David Yaro | Paul Georgescu https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 842 860 10.15388/namc.2021.26.24120 A mathematical model of population dynamics for the internet gaming addiction https://www.journals.vu.lt/nonlinear-analysis/article/view/24177 <p>As the number of internet users appears to steadily increase each year, Internet Gaming Disorder (IGD) is bound to increase as well. The question how this increase will take place, and what factors have the largest impact on this increase, naturally arises. We consider a system of ordinary differential equations as a simple mathematical model of the population dynamics about the internet gaming. We assume three stages about the internet gamer’s state: moderate, addictive, and under treatment. The transition of the gamer’s state between the moderate and the addictive stages is significantly affected by the social nature of internet gaming. As the activity of social interaction gets higher, the gamer would be more likely to become addictive. With the inherent social reinforcement of internet game, the addictive gamer would hardly recontrol his/herself to recover to the moderate gamer. Our result on the model demonstrates the importance of earlier initiation of a system to check the IGD and lead to some medical/therapeutic treatment. Otherwise, the number of addictive gamers would become larger beyond the socially controllable level.</p> Hiromi Seno Copyright (c) 2021 Hiromi Seno https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 861 883 10.15388/namc.2021.26.24177 Mathematical insights into neuroendocrine transdifferentiation of human prostate cancer cells https://www.journals.vu.lt/nonlinear-analysis/article/view/24441 <p>Prostate cancer represents the second most common cancer diagnosed in men and the fifth most common cause of death from cancer worldwide. In this paper, we consider a nonlinear mathematical model exploring the role of neuroendocrine transdifferentiation in human prostate cancer cell dynamics. Sufficient conditions are given for both the biological relevance of the model’s solutions and for the existence of its equilibria. By means of a suitable Liapunov functional the global asymptotic stability of the tumour-free equilibrium is proven, and through the use of sensitivity and bifurcation analyses we identify the parameters responsible for the occurrence of Hopf and saddle-node bifurcations. Numerical simulations are provided highlighting the behaviour discovered, and the results are discussed together with possible improvements to the model.</p> Leo Turner Andrew Burbanks Marianna Cerasuolo Copyright (c) 2021 Leo Turner | Andrew Burbanks | Marianna Cerasuolo https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 884 913 10.15388/namc.2021.26.24441 Existence of a unique solution for a third-order boundary value problem with nonlocal conditions of integral type https://www.journals.vu.lt/nonlinear-analysis/article/view/23932 <p>The existence of a unique solution for a third-order boundary value problem with integral condition is proved in several ways. The main tools in the proofs are the Banach fixed point theorem and the Rus’s fixed point theorem. To compare the applicability of the obtained results, some examples are considered.</p> Sergey Smirnov Copyright (c) 2021 Sergey Smirnov https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 914 927 10.15388/namc.2021.26.23932 Existence of positive S-asymptotically periodic solutions of the fractional evolution equations in ordered Banach spaces https://www.journals.vu.lt/nonlinear-analysis/article/view/24176 <p>In this paper, we discuss the asymptotically periodic problem for the abstract fractional evolution equation under order conditions and growth conditions. Without assuming the existence of upper and lower solutions, some new results on the existence of the positive <em>S</em>-asymptotically <em>ω</em>-periodic mild solutions are obtained by using monotone iterative method and fixed point theorem. It is worth noting that Lipschitz condition is no longer needed, which makes our results more widely applicable.</p> Qiang Li Lishan Liu Mei Wei Copyright (c) 2021 Qiang Li | Lishan Liu | Mei Wei https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 928 946 10.15388/namc.2021.26.24176 Time-periodic Poiseuille-type solution with minimally regular flow rate https://www.journals.vu.lt/nonlinear-analysis/article/view/24502 <p>The nonstationary Navier–Stokes equations are studied in the infinite cylinder <em>Π</em> = {<em>x</em> = (<em>x</em><span style="font-size: 11.6667px;">',</span>&nbsp;<em>x</em><sub>n</sub>) ∈ <em>R<sub>n</sub></em>:&nbsp; <em>x</em>' ∈ <em>σ</em> ∈ <em>R</em><sup><em>&nbsp;n </em>– 1</sup>: – ∞ &lt; <em>x</em><sub>n</sub> &lt; ∞, <em>n</em> = 2, 3} under the additional condition of the prescribed time-periodic flow-rate (flux) <em>F</em>(<em>t</em>). It is assumed that the flow-rate <em>F</em> belongs to the space <em>L</em><sup>2</sup>(0, 2<em>π</em>), only. The time-periodic Poiseuille solution has the form <em>u</em>(<em>x, t</em>) = (0, ... , 0, <em>U</em>(<em>x'</em>, <em>t</em>)),&nbsp; <em>p</em>(<em>x,t</em>) = –<em>q</em>(<em>t</em>)<em>x<sub>n</sub></em> + <em>p</em><sub>0</sub>(<em>t</em>), where (<em>U</em>(<em>x<span style="font-size: 11.6667px;">'</span></em>, <em>t</em>), <em>q</em>(<em>t</em>)) is a&nbsp;solution of an inverse problem for the time-periodic heat equation with a specific over-determination condition. The existence and uniqueness of a solution to this problem is proved.</p> Kristina Kaulakytė Nikolajus Kozulinas Konstantin Pileckas Copyright (c) 2021 Kristina Kaulakytė | Nikolajus Kozulinas | Konstantin Pileckas https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 947 968 10.15388/namc.2021.26.24502 Asymptotic analysis of Sturm–Liouville problem with nonlocal integral-type boundary condition https://www.journals.vu.lt/nonlinear-analysis/article/view/24299 <p>In this study, we obtain asymptotic formulas for eigenvalues and eigenfunctions of the one-dimensional Sturm–Liouville equation with one classical-type Dirichlet boundary condition and integral-type nonlocal boundary condition. We investigate solutions of special initial value problem and find asymptotic formulas of arbitrary order. We analyze the characteristic equation of the boundary value problem for eigenvalues and derive asymptotic formulas of arbitrary order. We apply the obtained results to the problem with integral-type nonlocal boundary condition.</p> Artūras Štikonas Erdoğan Şen Copyright (c) 2021 Artūras Štikonas | Erdoğan Şen https://creativecommons.org/licenses/by/4.0 2021-09-01 2021-09-01 26 5 969 991 10.15388/namc.2021.26.24299