Nonlinear Analysis: Modelling and Control https://www.journals.vu.lt/nonlinear-analysis <p>Founded in 1997. Journal provides a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature.&nbsp;</p> en-US <p>Please read the Copyright Notice in&nbsp;<a href="http://www.zurnalai.vu.lt/acta-paedagogica-vilnensia/journalpolicy">Journal Policy</a>.&nbsp;</p> nonlinear@mii.vu.lt (Prof. Feliksas Ivanauskas) vigintas.stancelis@kf.vu.lt (Vigintas Stancelis) Wed, 01 Jul 2020 00:00:00 +0000 OJS 3.1.2.1 http://blogs.law.harvard.edu/tech/rss 60 Exponential state estimation for competitive neural network via stochastic sampled-data control with packet losses https://www.journals.vu.lt/nonlinear-analysis/article/view/17803 <p>This paper investigates the exponential state estimation problem for competitive neural networks via stochastic sampled-data control with packet losses. Based on this strategy, a switched system model is used to describe packet dropouts for the error system. In addition, transmittal delays between neurons are also considered. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator with probabilistic sampling in two sampling periods is proposed. Then the estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs), which can be solved by using available software. When the missing of control packet occurs, some sufficient conditions are obtained to guarantee that the exponentially stable of the error system by means of constructing an appropriate Lyapunov function and using the average dwell-time technique. Finally, a numerical example is given to show the effectiveness of the proposed method.</p> Xin Sui | Yongqing Yang | Fei Wang Copyright (c) 2020 Xin Sui | Yongqing Yang | Fei Wang https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/17803 Wed, 01 Jul 2020 00:00:00 +0000 Minimization of entropy generation due to MHD double diffusive mixed convection in a lid driven trapezoidal cavity with various aspect ratios https://www.journals.vu.lt/nonlinear-analysis/article/view/16774 <p>Entropy generation minimization has significant importance in fluid flow, heat and mass transfer in an enclosure to get the maximum efficiency of a system and to reduce the loss of energy. In the present study, the analysis of mixed convection fluid flow, heat and mass transfer with heat line and mass line concept and entropy generation due to the effects of fluid flow, heat flow, mass flow and magnetic field in a trapezoidal enclosure with linearly heated and diffusive left wall, uniformly heated and diffusive lower wall, cold and nondiffusive right wall, adiabatic and zero diffusion gradient top wall have been reported. Parametric studies for the wide range of Prandtl number (<em>Pr</em> = 0.7 for air cooling system and <em>Pr</em> = 1000 for the engines filled with olive or engine oils), Rayleigh number (<em>Ra</em> = 10<sup>3</sup>–10<sup>5</sup>), aspect ratio (A = 0.5–1.5) and inclination angle of the cavity (<em>ϕ</em> = 45°–90°) have been performed, which help to construct the perfect shape of cavity in many engineering and physical applications so that the entropy is minimum to get the maximum efficiency of any system. The finite-difference approximation has been used to find out the numerical solutions. Biconjugate Gradient Stabilized (BiCGStab) method is used to solve the discretized nonhomogeneous system of linear equations.</p> Priyajit Mondal | Tapas Ray Mahapatra Copyright (c) 2020 Priyajit Mondal | Tapas Ray Mahapatra https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/16774 Wed, 01 Jul 2020 00:00:00 +0000 Persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations https://www.journals.vu.lt/nonlinear-analysis/article/view/18384 <p>In this paper, we develop the impulsive control theory to nonautonomous logistic system with time-varying delays. Some sufficient conditions ensuring the persistence of nonautonomous logistic system with time-varying delays and impulsive perturbations are derived. It is shown that the persistence of the considered system is heavily dependent on the impulsive perturbations. The proposed method of this paper is completely new. Two examples and the simulations are given to illustrate the proposed method and results.</p> Dan Yang | Xiaodi Li | Zhongmin Liu | Jinde Cao Copyright (c) 2020 Dan Yang | Xiaodi Li | Zhongmin Liu | Jinde Cao https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/18384 Wed, 01 Jul 2020 00:00:00 +0000 Some new fixed point results in rectangular metric spaces with an application to fractional-order functional differential equations https://www.journals.vu.lt/nonlinear-analysis/article/view/17928 <p>In this paper, we establish some new fixed point theorems for generalized <em>ϕ</em>–<em>ψ</em>-contractive mappings satisfying an admissibility-type condition in a Hausdorff rectangular metric space with the help of <em>C</em>-functions. In this process, we rectify the proof of Theorem 3.2 due to Budhia et al. [New fixed point results in rectangular metric space and application to fractional calculus, <em>Tbil. Math. J</em>., 10(1):91–104, 2017]. Some examples are given to illustrate the theorems. Finally, we apply our result (Corollary 3.6) to establish the existence of a solution for an initial value problem of a fractional-order functional differential equation with infinite delay.&nbsp;</p> Lokesh Budhia | Hassen Aydi | Arslan Hojat Ansari | Dhananjay Gopal Copyright (c) 2020 Lokesh Budhia | Hassen Aydi | Arslan Hojat Ansari | Dhananjay Gopal https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/17928 Wed, 01 Jul 2020 00:00:00 +0000 New extended generalized Kudryashov method for solving three nonlinear partial differential equations https://www.journals.vu.lt/nonlinear-analysis/article/view/17203 <p>New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics.</p> Elsayed M.E. Zayed | Reham M.A. Shohib | Mohamed E.M. Alngar Copyright (c) 2020 Elsayed M.E. Zayed | Reham M.A. Shohib | Mohamed E.M. Alngar https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/17203 Wed, 01 Jul 2020 00:00:00 +0000 Solvability of fractional dynamic systems utilizing measure of noncompactness https://www.journals.vu.lt/nonlinear-analysis/article/view/17896 <p>Fractional dynamics is a scope of study in science considering the action of systems. These systems are designated by utilizing derivatives of arbitrary orders. In this effort, we discuss the sufficient conditions for the existence of the mild solution (m-solution) of a class of fractional dynamic systems (FDS). We deal with a new family of fractional m-solution in R<sup>n</sup> for fractional dynamic systems. To accomplish it, we introduce first the concept of (<em>F,&nbsp;ψ</em>)-contraction based on the measure of noncompactness in some Banach spaces. Consequently, we establish requisite fixed point theorems (FPTs), which extend existing results following the Krasnoselskii FPT and coupled fixed point results as a outcomes of derived one. Finally, we give a numerical example to verify the considered FDS, and we solve it by iterative algorithm constructed by semianalytic method with high accuracy. The solution can be considered as bacterial growth system when the time interval is large.&nbsp;</p> Hemant Kumar Nashine | Rabha W. Ibrahim | Reza Arab | Mohsen Rabbani Copyright (c) 2020 Hemant Kumar Nashine | Rabha W. Ibrahim | Reza Arab | Mohsen Rabbani https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/17896 Wed, 01 Jul 2020 00:00:00 +0000 Turing instability and spatially homogeneous Hopf bifurcation in a diffusive Brusselator system https://www.journals.vu.lt/nonlinear-analysis/article/view/17437 <p>The present paper deals with a reaction–diffusion Brusselator system subject to the homogeneous Neumann boundary condition. When the effect of spatial diffusion is neglected, the local asymptotic stability and the detailed Hopf bifurcation of the unique positive equilibrium of the associated ODE system are analyzed. In the stable domain of the ODE system, the effect of spatial diffusion is explored, and local asymptotic stability, Turing instability and existence of Hopf bifurcation of the constant positive equilibrium are demonstrated. In addition, the direction of spatially homogeneous Hopf bifurcation and the stability of the spatially homogeneous bifurcating periodic solutions are also investigated. Finally, numerical simulations are also provided to check the obtained theoretical results.</p> Xiang-Ping Yan | Pan Zhang | Cun-Huz Zhang Copyright (c) 2020 Xiang-Ping Yan | Pan Zhang | Cun-Huz Zhang https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/17437 Wed, 01 Jul 2020 00:00:00 +0000 Controllability of conformable differential systems https://www.journals.vu.lt/nonlinear-analysis/article/view/18135 <p align="LEFT">This paper deals with complete controllability of systems governed by linear and semilinear conformable differential equations. By establishing conformable Gram criterion and rank criterion, we give sufficient and necessary conditions to examine that a linear conformable system is null completely controllable. Further, we apply Krasnoselskii’s fixed point theorem to derive a completely controllability result for a semilinear conformable system. Finally, three numerical examples are given to illustrate our theoretical results.</p> <p>&nbsp;</p> Xiaowen Wang | JinRong Wang | Michal Fečkan Copyright (c) 2020 Xiaowen Wang | JinRong Wang | Michal Fečkan https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/18135 Wed, 01 Jul 2020 00:00:00 +0000 Approximations for sums of three-valued 1-dependent symmetric random variables https://www.journals.vu.lt/nonlinear-analysis/article/view/16843 <p>The sum of symmetric three-point 1-dependent nonidentically distributed random variables is approximated by a compound Poisson distribution. The accuracy of approximation is estimated in the local and total variation norms. For distributions uniformly bounded from zero,<br>the accuracy of approximation is of the order <em>O</em>(<em>n</em><sup>–1</sup>). In the general case of triangular arrays of identically distributed summands, the accuracy is at least of the order <em>O</em>(<em>n<sup>–</sup></em><sup>1/2</sup>). Nonuniform estimates are obtained for distribution functions and probabilities. The characteristic function<br>method is used. &nbsp;</p> Gabija Liaudanskaitė | Vydas Čekanavičius Copyright (c) 2020 Gabija Liaudanskaitė | Vydas Čekanavičius https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/16843 Wed, 01 Jul 2020 00:00:00 +0000 Electroencephalogram spike detection and classification by diagnosis with convolutional neural network https://www.journals.vu.lt/nonlinear-analysis/article/view/18016 <p>This work presents convolutional neural network (CNN) based methodology for electroencephalogram (EEG) classification by diagnosis: benign childhood epilepsy with centrotemporal spikes (rolandic epilepsy) (Group I) and structural focal epilepsy (Group II). Manual classification of these groups is sometimes difficult, especially, when no clinical record is available, thus presenting a need for an algorithm for automatic classification. The presented algorithm has the following steps: (i) EEG spike detection by morphological filter based algorithm; (ii) classification of EEG spikes using preprocessed EEG signal data from all channels in the vicinity of the spike detected; (iii) majority rule classifier application to all EEG spikes from a single patient. Classification based on majority rule allows us to achieve 80% average accuracy (despite the fact that from a single spike one would obtain only 58% accuracy).&nbsp;</p> Andrius Vytautas Misiukas Misiūnas | Valdas Rapševičius | Rūta Samaitienė | Tadas Meškauskas Copyright (c) 2020 Andrius Vytautas Misiukas Misiūnas | Valdas Rapševičius | Rūta Samaitienė | Tadas Meškauskas https://creativecommons.org/licenses/by/4.0 https://www.journals.vu.lt/nonlinear-analysis/article/view/18016 Wed, 01 Jul 2020 00:00:00 +0000