Nonlinear Analysis: Modelling and Control

Journal Information
ISSN / EISSN : 1392-5113 / 1392-5113
Current Publisher: Vilnius University Press (10.15388)
Total articles ≅ 358
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Nonlinear Analysis: Modelling and Control, Volume 26, pp 534-549; doi:10.15388/namc.2021.26.23933

Abstract:
The task of identification of randomly scattered “bad” items in a fixed set of objects is a frequent one, and there are many ways to deal with it. “Group testing” (GT) refers to the testing strategy aiming to effectively replace the inspection of single objects by the inspection of groups spanning more than one object. First announced by Dorfman in 1943, the methodology has underwent vigorous development, and though many related research still take place, the ground ideas remain the same. In the present paper, we revisit two classical GT algorithms: the Dorfman’s algorithm and the halving algorithm. Our fresh treatment of the latter and expository comparison of the two is devoted to dissemination of GT ideas, which are so important in the current COVID-19 induced pandemic situation.
, , Shikun Bai, Yonghong Wu
Nonlinear Analysis: Modelling and Control, Volume 26, pp 502-521; doi:10.15388/namc.2021.26.22538

Abstract:
In this paper, we study a system of Hadamard fractional multi-point boundary value problems. We first obtain triple positive solutions when the nonlinearities satisfy some bounded conditions. Next, we also obtain a nontrivial solution when the nonlinearities can be asymptotically linear growth. Furthermore, we provide two examples to illustrate our main results.
Chengbo Zhai, Jing Ren
Nonlinear Analysis: Modelling and Control, Volume 26, pp 482-501; doi:10.15388/namc.2021.26.23055

Abstract:
This article is devoted to studying a nonhomogeneous boundary value problem involving Stieltjes integral for a more general form of the fractional q-difference equation with p(t)-Laplacian operator. Here p(t)-Laplacian operator is nonstandard growth, which has been used more widely than the constant growth operator. By using fixed point theorems of φ – (h, e)-concave operators some conditions, which guarantee the existence of a unique positive solution, are derived. Moreover, we can construct an iterative scheme to approximate the unique solution. At last, two examples are given to illustrate the validity of our theoretical results.
Roberta Hansen, Graciela A. González
Nonlinear Analysis: Modelling and Control, Volume 26, pp 419-439; doi:10.15388/namc.2021.26.23052

Abstract:
Based on existing feedback control methods such as OGY and Pyragas, alternative new schemes are proposed for stabilization of unstable periodic orbits of chaotic and hyperchaotic dynamical systems by suitable modulation of a control parameter. Their performances are improved with respect to: (i) robustness, (ii) rate of convergences, (iii) reduction of waiting time, (iv) reduction of noise sensitivity. These features are analytically investigated, the achievements are rigorously proved and supported by numerical simulations. The proposed methods result successful for stabilizing unstable periodic orbits in some classical discrete maps like 1-D logistic and standard 2-D Hénon, but also in the hyperchaotic generalized n-D Hénon-like maps.
Wenjun Liu, Weifan Zhao
Nonlinear Analysis: Modelling and Control, Volume 26, pp 396-418; doi:10.15388/namc.2021.26.23051

Abstract:
In this paper, we investigate the stabilization of a one-dimensional thermoelastic laminated beam with structural damping coupled with a heat equation modeling an expectedly dissipative effect through heat conduction governed by Gurtin–Pipkin thermal law. Under some assumptions on the relaxation function g, we establish the well-posedness of the problem by using Lumer–Phillips theorem. Furthermore, we prove the exponential stability and lack of exponential stability depending on a stability number by using the perturbed energy method and Gearhart–Herbst–Prüss–Huang theorem, respectively.
Rina Su, Chunrui Zhang
Nonlinear Analysis: Modelling and Control, Volume 26, pp 375-395; doi:10.15388/namc.2021.26.23050

Abstract:
In this paper, the Hopf-zero bifurcation of the ring unidirectionally coupled Toda oscillators with delay was explored. First, the conditions of the occurrence of Hopf-zero bifurcation were obtained by analyzing the distribution of eigenvalues in correspondence to linearization. Second, the stability of Hopf-zero bifurcation periodic solutions was determined based on the discussion of the normal form of the system, and some numerical simulations were employed to illustrate the results of this study. Lastly, the normal form of the system on the center manifold was derived by using the center manifold theorem and normal form method.
, Lakshmi Kanta Dey, , Stojan Radenovi´c
Nonlinear Analysis: Modelling and Control, Volume 26, pp 522-533; doi:10.15388/namc.2021.26.22497

Abstract:
In this manuscript, we establish two Wardowski–Feng–Liu-type fixed point theorems for orbitally lower semicontinuous functions defined in orbitally complete b-metric spaces. The obtained results generalize and improve several existing theorems in the literature. Moreover, the findings are justified by suitable nontrivial examples. Further, we also discuss ordered version of the obtained results. Finally, an application is presented by using the concept of fractal involving a certain kind of fractal integral equations. An illustrative example is presented to substantiate the applicability of the obtained result in reducing the energy of an antenna.
Dehua Wang, Xiao-Li Ding,
Nonlinear Analysis: Modelling and Control, Volume 26, pp 440-460; doi:10.15388/namc.2021.26.23053

Abstract:
This paper is concerned with the stability of fractional-order systems with randomly timevarying parameters. Two approaches are provided to check the stability of such systems in mean sense. The first approach is based on suitable Lyapunov functionals to assess the stability, which is of vital importance in the theory of stability. By an example one finds that the stability conditions obtained by the first approach can be tabulated for some special cases. For some complicated linear and nonlinear systems, the stability conditions present computational difficulties. The second alternative approach is based on integral inequalities and ingenious mathematical method. Finally, we also give two examples to demonstrate the feasibility and advantage of the second approach. Compared with the stability conditions obtained by the first approach, the stability conditions obtained by the second one are easily verified by simple computation rather than complicated functional construction. The derived criteria improve the existing related results.
Shuangrui Zhao, HongBin Wang, Weihua Jiang
Nonlinear Analysis: Modelling and Control, Volume 26, pp 461-481; doi:10.15388/namc.2021.26.23054

Abstract:
In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by analyzing the characteristic equation. For Turing–Hopf bifurcation, we derive the truncated third-order normal form based on the work of Jiang et al. [11], which is topologically equivalent to the original equation, and theoretically reveal system exhibits abundant spatial, temporal and spatiotemporal patterns, such as semistable spatially inhomogeneous periodic solutions, as well as tristable patterns of a pair of spatially inhomogeneous steady states and a spatially homogeneous periodic solution coexisting. Especially, we theoretically explain the phenomenon that time delay inhibits the formation of heterogeneous steady patterns, found by S. Lee, E. Gaffney and N. Monk [The influence of gene expression time delays on Gierer–Meinhardt pattern formation systems, Bull. Math. Biol., 72(8):2139–2160, 2010.]
Antanas Laurinčikas, Darius Šiaučiūnas, Monika Tekorė
Nonlinear Analysis: Modelling and Control, Volume 26, pp 550-564; doi:10.15388/namc.2021.26.23934

Abstract:
In the paper, a joint discrete universality theorem for periodic zeta-functions with multiplicative coefficients on the approximation of analytic functions by shifts involving the sequence f kg of imaginary parts of nontrivial zeros of the Riemann zeta-function is obtained. For its proof, a weak form of the Montgomery pair correlation conjecture is used. The paper is a continuation of [A. Laurinčikas, M. Tekorė, Joint universality of periodic zeta-functions with multiplicative coefficients, Nonlinear Anal. Model. Control, 25(5):860–883, 2020] using nonlinear shifts for approximation of analytic functions.
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