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> 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> Editorial Board https://www.journals.vu.lt/nonlinear-analysis/article/view/15305 Artūras Štikonas Copyright (c) 2019-12-06 2019-12-06 25 1 1 1 Nonlinear dynamics of full-range CNNs with time-varying delays and variable coefficients https://www.journals.vu.lt/nonlinear-analysis/article/view/15717 <p>In the article, the dynamical behaviours of the full-range cellular neural networks (FRCNNs) with variable coefficients and time-varying delays are considered. Firstly, the improved model of the FRCNNs is proposed, and the existence and uniqueness of the solution are studied by means of differential inclusions and set-valued analysis. Secondly, by using the Hardy inequality, the matrix analysis, and the Lyapunov functional method, we get some criteria for achieving the globally exponential stability (GES). Finally, some examples are provided to verify the correctness of the theoretical results.</p> Shuxin Liu Haijun Jiang Liwei Zhang Xuehui Mei Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 1–18 1–18 10.15388/namc.2020.25.15717 Dynamics of a diffusive predator–prey model with herd behavior https://www.journals.vu.lt/nonlinear-analysis/article/view/15723 <p>This paper is devoted to considering a diffusive predator–prey model with Leslie–Gower term and herd behavior subject to the homogeneous Neumann boundary conditions. Concretely, by choosing the proper bifurcation parameter, the local stability of constant equilibria of this model without diffusion and the existence of Hopf bifurcation are investigated by analyzing the distribution of the eigenvalues. Furthermore, the explicit formula for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solutions are also derived by applying the normal form theory. Next, we show the stability of positive constant equilibrium, the existence and stability of periodic solutions near positive constant equilibrium for the diffusive model. Finally, some numerical simulations are carried out to support the analytical results.</p> Yan Li Sanyun Li Fengrong Zhang Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 19–35 19–35 10.15388/namc.2020.25.15723 Global exponential synchronization of quaternion-valued memristive neural networks with time delays https://www.journals.vu.lt/nonlinear-analysis/article/view/15724 <p>This paper extends the memristive neural networks (MNNs) to quaternion field, a new class of neural networks named quaternion-valued memristive neural networks (QVMNNs) is then established, and the problem of drive-response global synchronization of this type of networks is investigated in this paper. Two cases are taken into consideration: one is with the conventional differential inclusion assumption, the other without. Criteria for the global synchronization of these two cases are achieved respectively by appropriately choosing the Lyapunov functional and applying some inequality techniques. Finally, corresponding simulation examples are presented to demonstrate the correctness of the proposed results derived in this paper.</p> Ruoyu Wei Jinde Cao Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 36–56 36–56 10.15388/namc.2020.25.15724 Destroying synchrony in an array of the FitzHugh–Nagumo oscillators by external DC voltage source https://www.journals.vu.lt/nonlinear-analysis/article/view/15727 <p>A control method for desynchronizing an array of mean-field coupled FitzHugh–Nagumo-type oscillators is described. The technique is based on applying an adjustable DC voltage source to the coupling node. Both, numerical solution of corresponding nonlinear differential equations and hardware experiments with a nonlinear electrical circuit have been performed.</p> Elena Adomaitienė Skaidra Bumelienė Gytis Mykolaitis Arūnas Tamaševičius Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 57–68 57–68 10.15388/namc.2020.25.15727 Stability analysis of partial differential variational inequalities in Banach spaces https://www.journals.vu.lt/nonlinear-analysis/article/view/15730 <p>In this paper, we study a class of partial differential variational inequalities. A general stability result for the partial differential variational inequality is provided in the case the perturbed parameters are involved in both the nonlinear mapping and the set of constraints. The main tools are theory of semigroups, theory of monotone operators, and variational inequality techniques.<br><br></p> Faming Guo Wei Li Yi-bin Xiao Stanisław Migórski Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 69–83 69–83 10.15388/namc.2020.25.15730 Mathematical analysis of an economic growth model with perfect-substitution technologies https://www.journals.vu.lt/nonlinear-analysis/article/view/15733 <p>The purpose of this paper is to highlight certain features of a dynamic optimisation problem in an economic growth model with environmental negative externalities that gives rise to a two-dimensional dynamical system. In particular, it is demonstrated that the dynamics of the model, which is based on a production function with perfect substitutability (perfect substitution technologies), admits a locally attracting equilibrium with a basin of attraction that may be considerably large, as it can extend up to the boundary of the system phase plane. Moreover, this model exhibits global indeterminacy because either equilibrium of the system can be selected according to agent expectation. Formulas for the calculation of the bifurcation coefficients of the system are derived, and a result on the existence of limit cycles is obtained. A numerical example is given to illustrate the results.</p> Paolo Russu Copyright (c) 2020 Author http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 84–107 84–107 10.15388/namc.2020.25.15733 On joint approximation of analytic functions by nonlinear shifts of zeta-functions of certain cusp forms https://www.journals.vu.lt/nonlinear-analysis/article/view/15734 <p>In the paper, joint discrete universality theorems on the simultaneous approximation of a collection of analytic functions by a collection of discrete shifts of zeta-functions attached to normalized Hecke-eigen cusp forms are obtained. These shifts are defined by means of nonlinear differentiable functions that satisfy certain growth conditions, and their combination on positive integers is uniformly distributed modulo 1.</p> Antanas Laurinčikas Darius Šiaučiūnas Adelė Vaiginytė Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 108–125 108–125 10.15388/namc.2020.25.15734 A sufficient and necessary condition of existence of blow-up radial solutions for a k-Hessian equation with a nonlinear operator https://www.journals.vu.lt/nonlinear-analysis/article/view/15736 <p>In this paper, we establish the results of nonexistence and existence of blow-up radial solutions for a <em>k</em>-Hessian equation with a nonlinear operator. Under some suitable growth conditions for nonlinearity, the result of nonexistence of blow-up solutions is established, a sufficient and necessary condition on existence of blow-up solutions is given, and some further results are obtained.&nbsp;</p> Xinguang Zhang Lishan Liu Yonghong Wu Yujun Cui Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 126–143 126–143 10.15388/namc.2020.25.15736 Optimization of the total production time by splitting complex manual assembly processes https://www.journals.vu.lt/nonlinear-analysis/article/view/15738 <p>In this article, the minimization of the learning content in the total processing time is studied. Research is based on manual automotive wiring harness assembly, with unstable demand, fluctuating order quantities and enormous product variety. Such instability in manual production environment results that assembly is always at the start-up or learning phase, thus, operational times are greater than standard and operational efficiency is significantly reduced. Since a lot of research is done on learning time calculation, there is still lacking studies that address learning time reduction in such production situation. The methodology proposed in this article addresses reduction of learning time by splitting and simplifying complex assemblies of automotive wiring harnesses. Experimental results from the company indicate that this approach enables to optimize learning time and increase operational efficiency.</p> Vytautas Kleiza Justinas Tilindis Copyright (c) 2020 Authors http://creativecommons.org/licenses/by/4.0 2020-01-10 2020-01-10 25 1 144–161 144–161 10.15388/namc.2020.25.15738