Nonlinear Analysis: Modelling and Control <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="">Journal Policy</a>.&nbsp;</p> Synchronization of chaotic delayed systems via intermittent control and its adaptive strategy <p>In this paper the problem of synchronization for delayed chaotic systems is considered based on aperiodic intermittent control. First, delayed chaotic systems are proposed via aperiodic adaptive intermittent control. Next, to cut down the control gain, a new generalized intermittent control and its adaptive strategy is introduced. Then, by constructing a piecewise Lyapunov auxiliary function and making use of piecewise analysis technique, some effective and novel criteria are obtained to ensure the global synchronization of delayed chaotic systems by means of the designed control protocols. At the end, two examples with numerical simulations are provided to verify the effectiveness of the theoretical results proposed scheme.</p> Mei Liu Jie Chen Haijun Jiang Zhiyong Yu Cheng Hu Binglong Lu Copyright (c) 2021 Mei Liu | Jie Chen | Haijun Jiang | Zhiyong Yu | Cheng Hu | Binglong Lu 2021-11-01 2021-11-01 26 6 993 1011 10.15388/namc.2021.26.24419 Modeling the effects of insecticides and external efforts on crop production <p>In this paper a nonlinear mathematical model is proposed and analyzed to understand the effects of insects, insecticides and external efforts on the agricultural crop productions. In the modeling process, we have assumed that crops grow logistically and decrease due to insects, which are wholly dependent on crops. Insecticides and external efforts are applied to control the insect population and enhance the crop production, respectively. The external efforts affect the intrinsic growth rate and carrying capacity of crop production. The feasibility of equilibria and their stability properties are discussed. We have identified the key parameters for the formulation of effective control strategies necessary to combat the insect population and increase the crop production using the approach of global sensitivity analysis. Numerical simulation is performed, which supports the analytical findings. It is shown that periodic oscillations arise through Hopf bifurcation as spraying rate of insecticides decreases. Our findings suggest that to gain the desired crop production, the rate of spraying and the quality of insecticides with proper use of external efforts are much important.</p> A.K. Misra Rahul Patel Navnit Jha Copyright (c) 2021 A.K. Misra | Rahul Patel | Navnit Jha 2021-11-01 2021-11-01 26 6 1012 1030 10.15388/namc.2021.26.24442 Relative controllability of a stochastic system using fractional delayed sine and cosine matrices <p>In this paper, we study the relative controllability of a fractional stochastic system with pure delay in finite&nbsp; dimensional stochastic spaces. A set of sufficient conditions is obtained for relative exact controllability using fixed point theory, fractional calculus (including fractional delayed linear operators and Grammian matrices) and local assumptions on nonlinear terms. Finally, an example is given to illustrate our theory.</p> JinRong Wang T. Sathiyaraj Donal O’Regan Copyright (c) 2021 JinRong Wang | T. Sathiyaraj | Donal O’Regan 2021-11-01 2021-11-01 26 6 1031 1051 10.15388/namc.2021.26.24265 Study on evolution of a predator–prey model in a polluted environment <p>In this paper, we investigate the effects of pollution on the body size of prey about a predator–prey evolutionary model with a continuous phenotypic trait in a pulsed pollution discharge environment. Firstly, an eco-evolutionary predator–prey model incorporating the rapid evolution is formulated to investigate the effects of rapid evolution on the population density and the body size of prey by applying the quantitative trait evolutionary theory. The results show that rapid evolution can increase the density of prey and avoid population extinction, and with the worsening of pollution, the evolutionary traits becomes smaller gradually. Next, by employing the adaptive dynamic theory, a long-term evolutionary model is formulated to evaluate the effects of long-term evolution on the population dynamics and the effects of pollution on the body size of prey. The invasion fitness function is given, which reflects whether the mutant can invade successfully or not. Considering the trade-off between the intrinsic growth rate and the evolutionary trait, the critical function analysis method is used to investigate the dynamics of such slow evolutionary system. The results of theoretical analysis and numerical simulations conclude that pollution affects the evolutionary traits and evolutionary dynamics. The worsening of the pollution leads to a smaller body size of prey due to natural selection, while the opposite is more likely to generate evolutionary branching.</p> Bing Liu Xin Wang Le Song Jingna Liu Copyright (c) 2021 Bing Liu | Xin Wang | Le Song | Jingna Liu 2021-11-01 2021-11-01 26 6 1052 1070 10.15388/namc.2021.26.24148 Analysis of fractional hybrid differential equations with impulses in partially ordered Banach algebras <p>In this paper, we investigate a class of fractional hybrid differential equations with impulses, which can be seen as nonlinear differential equations with a quadratic perturbation of second type and a linear perturbation in partially ordered Banach algebras. We deduce the existence and approximation of a mild solution for the initial value problems of this system by applying Dhage iteration principles and related hybrid fixed point theorems. Compared with previous works, we generalize the results to fractional order and extend some existing conclusions for the first time. Meantime, we take into consideration the effect of impulses. Our results indicate the influence of fractional order for nonlinear hybrid differential equations and improve some known results, which have wider applications as well. A numerical example is included to illustrate the effectiveness of the proposed results.</p> Jin You Zhenlai Han Copyright (c) 2021 Jin You | Zhenlai Han 2021-11-01 2021-11-01 26 6 1071 1086 10.15388/namc.2021.26.24939 On the boundary value problems of piecewise differential equations with left-right fractional derivatives and delay <p>In this paper, we study the multi-point boundary value problems for a new kind of piecewise differential equations with left and right fractional derivatives and delay. In this system, the state variables satisfy the different equations in different time intervals, and they interact with each other through positive and negative delay. Some new results on the existence, no-existence and multiplicity for the positive solutions of the boundary value problems are obtained by using Guo–Krasnoselskii’s fixed point theorem and Leggett–Williams fixed point theorem. The results for existence highlight the influence of perturbation parameters. Finally, an example is given out to illustrate our main results.</p> Yuxin Zhang Xiping Liu Mei Jia Copyright (c) 2021 Yuxin Zhang | Xiping Liu | Mei Jia 2021-11-01 2021-11-01 26 6 1087 1105 10.15388/namc.2021.26.24622 Feedback exponential stabilization of the semilinear heat equation with nonlocal initial conditions <p>The present paper is devoted to the problem of stabilization of the one-dimensional semilinear heat equation with nonlocal initial conditions. The control is with boundary actuation. It is linear, of finite-dimensional structure, given in an explicit form. It allows to write the corresponding solution of the closed-loop equation in a mild formulation via a kernel, then to apply a fixed point argument in a convenient space.</p> Ionuţ Munteanu Copyright (c) 2021 Ionu¸t Munteanu 2021-11-01 2021-11-01 26 6 1106 1122 10.15388/namc.2021.26.24809 Entropy generation for MHD natural convection in enclosure with a micropolar fluid saturated porous medium with Al2O3Cu water hybrid nanofluid <p>This contribution gives a numerical investigation of buoyancy-driven flow of natural convection heat transfer and entropy generation of non-Newtonian hybrid nanofluid (Al<sub>2</sub>O<sub>3</sub>-Cu) within an enclosure square porous cavity. Hybrid nanofluids represent a novel type of enhanced active fluids. During the current theoretical investigation, an actual available empirical data for both thermal conductivity and dynamic viscosity of hybrid nanofluids are applied directly. Numerical simulation have been implemented for solid nanoparticles, the volumetric concentration of which varies from 0.0% (i.e., pure fluid) to 0.1% of hybrid nanofluids. Heat and sink sources are situated on a part of the left and right sides of the cavity with length <em>B</em>, while the upper and bottom horizontal sides are kept adiabatic. The stated partial differential equations describing the flow are mutated to a dimensionless formulas, then solved numerically via the help of an implicit finite difference approach. The acquired computations are given in terms of streamlines, isotherms, isomicrorotations, isoconcentraions, local Began number, total entropy, local and mean Nusselt numbers. The data illustrates that variations of ratio of the average Nusselt number to the average Nusselt of pure fluid <em>Nu<sub>m</sub></em><sup>+</sup> is a decreasing function of <em>Ha</em> and <em>φ</em>, while <em>e</em><sup>+</sup> is an increasing function of <em>Ha</em> and <em>φ</em> parameters of hybrid nanofluid.</p> A. Mahdy S.E. Ahmed M.A. Mansour Copyright (c) 2021 A. Mahdy | S.E. Ahmed | M.A. Mansour 2021-11-01 2021-11-01 26 6 1123 1143 10.15388/namc.2021.26.24940 Hidden maximal monotonicity in evolutionary variational-hemivariational inequalities <p>In this paper, we propose a new methodology to study evolutionary variational-hemivariational inequalities based on the theory of evolution equations governed by maximal monotone operators. More precisely, the proposed approach, based on a hidden maximal monotonicity, is used to explore the well-posedness for a class of evolutionary variational-hemivariational inequalities involving history-dependent operators and related problems with periodic and antiperiodic boundary conditions. The applicability of our theoretical results is illustrated through applications to a fractional evolution inclusion and a dynamic semipermeability problem.</p> Emilio Vilches Shengda Zeng Copyright (c) 2021 Emilio Vilches | Shengda Zeng 2021-11-01 2021-11-01 26 6 1144 1165 10.15388/namc.2021.26.24941 Steady state non-Newtonian flow with strain rate dependent viscosity in domains with cylindrical outlets to infinity <p>The paper deals with a stationary non-Newtonian flow of a viscous fluid in unbounded domains with cylindrical outlets to infinity. The viscosity is assumed to be smoothly dependent on the gradient of the velocity. Applying the generalized Banach fixed point theorem, we prove the existence, uniqueness and high order regularity of solutions stabilizing in the outlets to the prescribed quasi-Poiseuille flows. Varying the limit quasi-Poiseuille flows, we prove the stability of the solution.</p> Grigory Panasenko Konstantin Pileckas Bogdan Vernescu Copyright (c) 2021 Grigory Panasenko | Konstantin Pileckas | Bogdan Vernescu 2021-11-01 2021-11-01 26 6 1166 1199 10.15388/namc.2021.26.24600 Asymptotic formulas for the left truncated moments of sums with consistently varying distributed increments <p>In this paper, we consider the sum <em>S<sub>n</sub><sup>ξ</sup></em> = <em>ξ</em><sub>1</sub> + ... + <em>ξ</em><sub>n</sub> of possibly dependent and nonidentically distributed real-valued random variables <em>ξ</em><sub>1</sub>, ... , <em>ξ</em><sub>n</sub> with consistently varying distributions. By assuming that collection {<em>ξ</em><sub>1</sub>, ... , <em>ξ</em><sub>n</sub>} follows the dependence structure, similar to the asymptotic independence, we obtain the asymptotic relations for <strong>E</strong>((<em>S<sub>n</sub>ξ</em>)<sup><em>α</em></sup><strong>1(</strong><em>S</em><sub><em>n</em></sub><sup><em>ξ</em></sup> &gt; <em>x</em>)) and <strong>E</strong>((<em>S<sub>n</sub><sup>ξ</sup></em> – <em>x</em>)<sup>+</sup>)<sup><em>α</em></sup>, where <em>α</em> is an arbitrary nonnegative real number. The obtained results have applications in various fields of applied probability, including risk theory and random walks.</p> Jonas Sprindys Jonas Šiaulys Copyright (c) 2021 Jonas Sprindys | Jonas Šiaulys 2021-11-01 2021-11-01 26 6 1200 1212 10.15388/namc.2021.26.24608