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> Existence of multiple positive solutions for a class of infinite-point singular p-Laplacian fractional differential equation with singular source terms https://www.journals.vu.lt/nonlinear-analysis/article/view/26363 <p>Based on properties of Green’s function and by Avery–Peterson fixed point theorem, the existence of multiple positive solutions are obtained for singular p-Laplacian fractional differential equation with infinite-point boundary conditions, and an example is given to demonstrate the validity of our main results.</p> Limin Guo Jingbo Zhao Lianying Liao Lishan Liu Copyright (c) 2022 Limin Guo | Jingbo Zhao | Lianying Liao | Lishan Liu https://creativecommons.org/licenses/by/4.0 2022-02-22 2022-02-22 27 1 21 10.15388/namc.2022.27.26363 How to empower Grünwald–Letnikov fractional difference equations with available initial condition? https://www.journals.vu.lt/nonlinear-analysis/article/view/26623 <p>In this paper, the initial condition independence property of Grünwald–Letnikov fractional difference is revealed for the first time. For example, the solution <em>x</em>(<em>k</em>) of equation <em><sub>a</sub></em><sup>G</sup>∇<em><sub>k</sub><sup>α</sup>x</em>(<em>k</em>) = <em>f</em>(<em>x</em>(<em>k</em>)),&nbsp; <em>k</em> &gt; <em>a</em> + 1, cannot be calculated with initial condition <em>x</em>(<em>a</em>). First, the initial condition independence property is carefully investigated in both time domain and frequency domain. Afterwards, some possible schemes are formulated to make the considered system connect to initial condition. Armed with this information, the concerned property is examined on three modified Grünwald–Letnikov definitions. Finally, results from illustrative examples demonstrate that the developed schemes are sharp.</p> Yiheng Wei Jinde Cao Chuang Li Yangquan Chen Copyright (c) 2022 Yiheng Wei | Jinde Cao | Chuang Li | Yangquan Chen https://creativecommons.org/licenses/by/4.0 2022-04-05 2022-04-05 27 1 19 10.15388/namc.2022.27.26623 Dufour and Soret effects on pulsatile hydromagnetic flow of Casson fluid in a vertical non-Darcian porous space https://www.journals.vu.lt/nonlinear-analysis/article/view/26678 <p>This article aims to inspect the pulsating hydromagnetic slip flow of Casson fluid in a vertical porous channel with heat and mass transfer. The fluid is injected into the channel from the left wall and removed at the opposite wall with the same velocity. The impact of non-Darcy, Soret, and Dufour effects are taken under consideration. The governing partial differential equations (PDEs) are converted to ordinary differential equations (ODEs) using perturbation method and solved by utilizing 4th-order Runge–Kutta (R–K) technique together with shooting method. The impact of dissimilar parameters on flow, heat and mass transfer characteristics are displayed and discussed.</p> Suripeddi Srinivas Challa Kalyan Kumar Anala Subramanyam Reddy Copyright (c) 2022 Suripeddi Suripeddi Srinivas | Challa Kalyan Kumar | Anala Subramanyam Reddy https://creativecommons.org/licenses/by/4.0 2022-04-11 2022-04-11 27 1 15 10.15388/namc.2022.27.26678 Predefined-time synchronization of 5D Hindmarsh–Rose neuron networks via backstepping design and application in secure communication https://www.journals.vu.lt/nonlinear-analysis/article/view/26557 <p>In this paper, the fast synchronization problem of 5D Hindmarsh–Rose neuron networks is studied. Firstly, the global predefined-time stability of a class of nonlinear dynamical systems is investigated under the complete beta function. Then an active controller via backstepping design is proposed to achieve predefined-time synchronization of two 5D Hindmarsh–Rose neuron networks in which the synchronization time of each state variable of the master-slave 5D Hindmarsh–Rose neuron networks is different and can be defined in advance, respectively. To show the applicability of the obtained theoretical results, the designed predefined-time backstepping controller is applied to secure communication to realize asynchronous communication of multiple different messages. Three numerical simulations are provided to validate the theoretical results.</p> Lixiong Lin Copyright (c) 2022 Lixiong Lin https://creativecommons.org/licenses/by/4.0 2022-04-13 2022-04-13 27 1 20 10.15388/namc.2022.27.26557 Effects of Joule heating, thermal radiation on MHD pulsating flow of a couple stress hybrid nanofluid in a permeable channel https://www.journals.vu.lt/nonlinear-analysis/article/view/26741 <p>The current work deals with the pulsatile hydromagnetic flow of blood-based couple stress hybrid nanofluid in a porous channel. For hybrid nanofluid, the fusion of gold (Au) and copper oxide (CuO) nanoparticles are suspended to the blood (base fluid). In this model, the employment of viscous dissipation, radiative heat, and Ohmic heating is incorporated. The governing flow equations (set of partial differential equations) are modernized to set of ordinary differential equations by using the perturbation technique. The nondimensional governing equations are solved by adopting the shooting procedure with the help of the Runge–Kutta fourth-order approach. Temperature distributions of hybrid nanofluid and conventional mono nanofluids are portrayed via pictorial results to claim that the hybrid nanofluid has better temperature distribution than mono nanofluids. Temperature is raising for the magnifying viscous dissipation, whereas the reverse behavior can be found with a rise in couple stress parameter. The heat transfer rate is getting high for the higher values of the Eckert number, and the same behavior is noticed with the uplifting magnetic field.</p> Somasundaram Rajamani Anala Subramanyam Reddy Copyright (c) 2022 Somasundaram Rajamani | Anala Subramanyam Reddy https://creativecommons.org/licenses/by/4.0 2022-04-13 2022-04-13 27 1 16 10.15388/namc.2022.27.26741 Exponential synchronization for second-order switched quaternion-valued neural networks with neutral-type and mixed time-varying delays https://www.journals.vu.lt/nonlinear-analysis/article/view/27326 <p>This article focuses on the global exponential synchronization (GES) for second-order state-dependent switched quaternion-valued neural networks (SOSDSQVNNs) with neutral-type and mixed delays. By proposing some new Lyapunov–Krasovskii functionals (LKFs) and adopting some inequalities, several new criteria in the shape of algebraic inequalities are proposed to ensure the GES for the concerned system by using hybrid switched controllers (HSCs). Different from the common reducing order and separation ways, this article presents some new LKFs to straightway discuss the GES of the concerned system based on non-reduction order and nonseparation strategies. Ultimately, an example is provided to validate the effectiveness of the theoretical outcomes.</p> Tingting Zhang Jigui Jian Copyright (c) 2022 Tingting Zhang | Jigui Jian https://creativecommons.org/licenses/by/4.0 2022-04-20 2022-04-20 27 1 19 10.15388/namc.2022.27.27326 Positive almost periodicity on SICNNs incorporating mixed delays and D operator https://www.journals.vu.lt/nonlinear-analysis/article/view/27417 <p>This article involves a kind of shunting inhibitory cellular neural networks incorporating D operator and mixed delays. First of all, we demonstrate that, under appropriate external input conditions, some positive solutions of the addressed system exist globally. Secondly, with the help of the differential inequality techniques and exploiting Lyapunov functional approach, some criteria are established to evidence the globally exponential stability on the positive almost periodic solutions. Eventually, a numerical case is provided to test and verify the correctness and reliability of the proposed findings.</p> Chuangxia Huang Bingwen Liu Hedi Yang Jinde Cao Copyright (c) 2022 Chuangxia Huang | Bingwen Liu | Hedi Yang | Jinde Cao https://creativecommons.org/licenses/by/4.0 2022-04-27 2022-04-27 27 1 21 10.15388/namc.2022.27.27417 Modeling and analysis of SIR epidemic dynamics in immunization and cross-infection environments: Insights from a stochastic model https://www.journals.vu.lt/nonlinear-analysis/article/view/27446 <p>We propose a stochastic SIR model with two different diseases cross-infection and immunization. The model incorporates the effects of stochasticity, cross-infection rate and immunization. By using stochastic analysis and Khasminski ergodicity theory, the existence and boundedness of the global positive solution about the epidemic model are firstly proved. Subsequently, we theoretically carry out the sufficient conditions of stochastic extinction and persistence of the diseases. Thirdly, the existence of ergodic stationary distribution is proved. The results reveal that white noise can affect the dynamics of the system significantly. Finally, the numerical simulation is made and consistent with the theoretical results.</p> Zhengbo Chang Xinzhu Meng Tasawar Hayat Aatef Hobiny Copyright (c) 2022 Zhengbo Chang | Xinzhu Meng | Tasawar Hayat | Aatef Hobiny https://creativecommons.org/licenses/by/4.0 2022-05-02 2022-05-02 27 1 26 10.15388/namc.2022.27.27446 Turing instability and pattern formation of a fractional Hopfield reaction–diffusion neural network with transmission delay https://www.journals.vu.lt/nonlinear-analysis/article/view/27473 <p>It is well known that integer-order neural networks with diffusion have rich spatial and temporal dynamical behaviors, including Turing pattern and Hopf bifurcation. Recently, some studies indicate that fractional calculus can depict the memory and hereditary attributes of neural networks more accurately. In this paper, we mainly investigate the Turing pattern in a delayed reaction–diffusion neural network with Caputo-type fractional derivative. In particular, we find that this fractional neural network can form steadily spatial patterns even if its first-derivative counterpart cannot develop any steady pattern, which implies that temporal fractional derivative contributes to pattern formation. Numerical simulations show that both fractional derivative and time delay have influence on the shape of Turing patterns.</p> Jiazhe Lin Jiapeng Li Rui Xu Copyright (c) 2022 Jiazhe Lin | Jiapeng Li | Rui Xu https://creativecommons.org/licenses/by/4.0 2022-05-05 2022-05-05 27 1 18 10.15388/namc.2022.27.27473 Finite-time reliable nonfragile control for fractionalorder nonlinear systems with asymmetrical saturation and structured uncertainties https://www.journals.vu.lt/nonlinear-analysis/article/view/27486 <p>This paper investigates the finite-time stabilization problem of fractional-order nonlinear differential systems via an asymmetrically saturated reliable control in the sense of Caputo’s fractional derivative. In particular, an asymmetrical saturation control problem is converted to a symmetrical saturation control problem by using a linear matrix inequality framework criterion to achieve the essential results. Specifically, in this paper, we obtain two sets of sufficient conditions under different scenarios of structured uncertainty, namely, norm-bounded parametric uncertainty and linear fractional transformation uncertainty. The uncertainty considered in this paper is a combination of polytopic form and structured form. With the help of control theories of fractional-order system and linear matrix inequality technique, some sufficient criteria to ensure reliable finite-time stability of fractional-order differential systems by using the indirect Lyapunov approach are derived. As a final point, the derived criteria are numerically validated by means of examples based on financial fractional-order differential system and permanent magnet synchronous motor chaotic fractional-order differential system.</p> L. Susana Ramya Rathinasamy Sakthivel Chao Wang Copyright (c) 2022 L. Susana Ramya | Rathinasamy Sakthivel | Chao Wang https://creativecommons.org/licenses/by/4.0 2022-05-09 2022-05-09 27 1 23 10.15388/namc.2022.27.27486 An upper-lower solution method for the eigenvalue problem of Hadamard-type singular fractional differential equation https://www.journals.vu.lt/nonlinear-analysis/article/view/27491 <p>In this paper, we are concerned with the eigenvalue problem of Hadamard-type singular fractional differential equations with multi-point boundary conditions. By constructing the upper and lower solutions of the eigenvalue problem and using the properties of the Green function, the eigenvalue interval of the problem is established via Schauder’s fixed point theorem. The main contribution of this work is on tackling the nonlinearity which possesses singularity on some space variables.</p> Xinguang Zhang Dezhou Kong Hui Tian Yonghong Wu Benchawan Wiwatanapataphee Copyright (c) 2022 Xinguang Zhang | Dezhou Kong | Hui Tian | Yonghong Wu | Benchawan Wiwatanapataphee https://creativecommons.org/licenses/by/4.0 2022-05-10 2022-05-10 27 1 14 10.15388/namc.2022.27.27491 Index spaces and standard indices in metric modelling https://www.journals.vu.lt/nonlinear-analysis/article/view/27493 <p>We analyze the basic structure of certain metric models, which are constituted by an index <em>I</em> acting on a metric space (<em>D</em>; <em>d</em>) representing a relevant property of the elements of <em>D</em>. We call such a structure (<em>D</em>; <em>d</em>; <em>I</em>) an index space and define on it normalization and consistency constants that measure to what extent I is compatible with the metric d. The “best” indices are those with such constants equal to 1 (standard indices), and we show an approximation method for other indices using them. With the help of Lipschitz extensions, we show how to apply these tools: a new model for the triage process in the emergency department of a hospital is presented.</p> Ezgi Erdoğan Antonia Ferrer-Sapena Eduardo Jiménez-Fernández Copyright (c) 2022 Ezgi Erdoğan | Antonia Ferrer-Sapena | Eduardo Jiménez-Fernández https://creativecommons.org/licenses/by/4.0 2022-05-10 2022-05-10 27 1 20 10.15388/namc.2022.27.27493 Spatiotemporal dynamics of a diffusive predator–prey model with fear effect https://www.journals.vu.lt/nonlinear-analysis/article/view/27535 <p>This paper concerned with a diffusive predator–prey model with fear effect. First, some basic dynamics of system is analyzed. Then based on stability analysis, we derive some conditions for stability and bifurcation of constant steady state. Furthermore, we derive some results on the existence and nonexistence of nonconstant steady states of this model by considering the effect of diffusion. Finally, we present some numerical simulations to verify our theoretical results. By mathematical and numerical analyses, we find that the fear can prevent the occurrence of limit cycle oscillation and increase the stability of the system, and the diffusion can also induce the chaos in the system.</p> Jia Liu Yun Kang Copyright (c) 2022 Jia Liu | Yun Kang https://creativecommons.org/licenses/by/4.0 2022-05-14 2022-05-14 27 1 22 10.15388/namc.2022.27.27535 Infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy–Sobolev–Maz’ya terms https://www.journals.vu.lt/nonlinear-analysis/article/view/27538 <p>In this paper, we consider the existence of infinitely many sign-changing solutions for an elliptic equation involving double critical Hardy–Sobolev–Maz’ya terms. By using a compactness result obtained in [C.H. Wang, J. Yang, Infinitely many solutions for an elliptic problem with double Hardy–Sobolev–Maz’ya terms, <em>Discrete Contin. Dyn. Syst.</em>, 36(3):1603–1628, 2016], we prove the existence of these solutions by a combination of invariant sets method and Ljusternik–Schnirelman-type minimax method.</p> Lixia Wang Pingping Zhao Dong Zhang Copyright (c) 2022 Lixia Wang | Pingping Zhao | Dong Zhang https://creativecommons.org/licenses/by/4.0 2022-05-15 2022-05-15 27 1 16 10.15388/namc.2022.27.27538 Controllability of nonlinear higher-order fractional damped stochastic systems involving multiple delays https://www.journals.vu.lt/nonlinear-analysis/article/view/27587 <p>This paper is concerned with the controllability problem for higher-order fractional damped stochastic systems with multiple delays, which involves fractional Caputo derivatives of any different orders. In the process of proof, we have proposed the controllability of considered linear system by establishing a controllability Grammian matrix and employing a control function. Sufficient conditions for the considered nonlinear system concerned to be controllable have been derived by constructing a proper control function and utilizing the Banach fixed point theorem with Burkholder–Davis–Gundy’s inequality. Finally, two examples are provided to emphasize the applicability of the derived results.</p> Ganesan Arthi Kalaiselvan Suganya Juan J. Nieto Copyright (c) 2022 Ganesan Arthi | Kalaiselvan Suganya | Juan J. Nieto https://creativecommons.org/licenses/by/4.0 2022-05-24 2022-05-24 27 1 25 10.15388/namc.2022.27.27587