Nonlinear Analysis: Modelling and Control
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Comparative approaches to solving the (2 + 1)-dimensional generalized coupled nonlinear Schrödinger equations with four-wave mixing
Full text linkThis paper extensively studies the propagation of optical solitons within the framework of (2 + 1)-dimensional generalized coupled nonlinear Schrödinger equations. The investigation employs three worldly integration techniques: the enhanced direct algebraic method, the enhanced Kudryashov method, and the new projective Riccati equation method. Through the application of these methods, a broad spectrum of soliton solutions has been uncovered, including bright, dark, singular, and straddled solitons. Additionally, this study reveals solutions characterized by Jacobi andWeierstrass elliptic functions, enriching the understanding of the dynamics underpinning optical solitons in complex systems. The diversity of the soliton solutions obtained demonstrates the versatility and efficacy of the employed integration techniques and contributes significantly to the theoretical and practical knowledge of nonlinear optical systems
New formulation of Lyapunov direct method for nonautonomous real-order systems
Full text linkLyapunov stability analysis of nonautonomous real-order systems is put forward here in the sense of Caputo in a new and different way. We introduce new theorems and inequalities that give stability of constant solutions in the domain of attraction to such systems when attached with random initial time placed on the real axis. We give some examples including an advanced nonlinear Lorenz system to illustrate the results
Finite-time stability of discrete fractional uncertain recurrent neural networks
Full text linkThis paper investigates finite-time stability of fractional uncertain difference equations with time delay. A fractional sum inequality is obtained from uncertain initial-value conditions. A delayed discrete Gronwall’s inequality is used, and sample paths are numerically illustrated. Finally, finite-time stability results are obtained for a fractional uncertain recurrent neural network model. It can be concluded that this paper provides an efficient tool for finite-time analysis of high-dimensional fractional uncertain systems with time delay
Soliton stability and topological invariants in a generalized nonlinear Klein–Gordon equation: Existence, dynamics, and conservation laws
Full text linkThis paper investigates the stability and dynamical behavior of soliton solutions in generalized nonlinear Klein–Gordon equations defined on higher-dimensional manifolds. We establish the existence of stable multisoliton configurations using variational methods and demonstrate their stability under small perturbations through energy estimates and topological considerations. Furthermore, we explore topological invariants (particularly, the topological charge) in preventing certain types of instabilities and ensuring the long-term persistence of solitons
M-matrices and one-dimensional discrete Sturm–Liouville problems with nonlocal boundary conditions
Full text linkThis article is the second part of a survey dedicated to M-matrices and the application of the finite difference method to elliptic problems with nonlocal boundary conditions. Here, we examine cases in which the matrix of the resulting system of linear equations is an M-matrix. Here, we address the discrete Sturm–Liouville problem with nonlocal boundary conditions, describing its spectrum in one-dimensional case. This enables us to determine the values of the nonlocality parameters for which the finite difference scheme is represented by an M-matrix
A few generalizations of Kendall’s tau. Part II: Intrinsic meaning, properties, and computational aspects
Full text linkContinuing our investigation on generalizations of Kendall’s τ, started in Part I of the paper, here we elaborate on the intrinsic meaning and degree of such polynomial-type concordance measures, as well as present many examples of their computation. In particular, we interpret generalized Kendall’s τφ as the difference between the average capacities of concordance and discordance, and, for power-type distortion functions φ, we obtain polynomial-type concordance measures of various degree, which could stimulate further research of their characterization as achieved for degree-one polynomial-type concordance measures by Taylor, Edwards, and Mikusiński
On a novel semigroup of enriched Chatterjea-type mappings in Banach spaces with a numerical experiment
Full text linkRecently in [V. Berinde and M. Păcurar, Approximating fixed points of enriched Chatterjea contractions by Krasnoselskij iterative algorithm in Banach spaces, J. Fixed Point Theory Appl., 23(4):66, 2021], using the technique of enrichment of contractive mappings by Krasnoselskij averaging, Berinde and Păcurar introduced a new type of mappings, called enriched Chatterjea-type mappings. The main aim of this article is to introduce a new semigroup of enriched Chatterjea-type mappings. We also establish weak and strong convergence results for enriched Chatterjea-type semigroups using a novel iterative process in uniformly convex Banach spaces. To support the theoretical results, we conduct numerical experiments demonstrating the convergence behavior of the iterative scheme under various initial conditions and control sequences. The findings confirm exponential convergence and highlight the effectiveness and robustness of the proposed method for common fixed point approximation
A new dynamic model for simultaneous saccharification and fermentation process of rice wine
Full text linkIn this paper, a new fractional model for the simultaneous saccharification and fermentation process of rice wine is proposed. To begin with, the existence and uniqueness of solution to the new model are proved by using some fixed point theorems. In addition, the stability at the equilibrium point and the Ulam–Hyers stability of the fractional simultaneous and saccharification fermentation model are analyzed. Then the approximate solutions of the fractional simultaneous saccharification and fermentation model are obtained by using the generalised Euler method. Finally, numerical simulations are given to verify the rationality of the fractional simultaneous saccharification and fermentation model. The new model proposed in this paper can more sensitively capture changes in the reaction
Notes on the losses compensation of a three-phase power system with DC offset based on geometric algebras
Full text linkIn a three-phase symmetric power system, we propose a transformation that converts the original current to a current with minimal losses while preserving the standard constraints. The selected transformation is realized in suitable geometric algebra and is not time-dependent. The proposed transformation uses the group symmetry of conformal geometric algebra, mainly rotations and tations
Fixed point results for single and multivalued three-points contractions
Full text linkIn this paper, we are concerned with the study of the existence of fixed points for single and multivalued three-points contractions. Namely, we first introduce a new class of singlevalued mappings defined on a metric space equipped with three metrics. A fixed point theorem is established for such mappings. The obtained result recovers that established recently by the second author [E. Petrov, Fixed point theorem for mappings contracting perimeters of triangles, J. Fixed Point Theory Appl., 25(3):74, 2023] for the class of single-valued mappings contracting perimeters of triangles. We next extend our study by introducing the class of multivalued three points contractions. A fixed point theorem, which is a multivalued version of that obtained in the above reference, is established. Some examples showing the validity of our obtained results are provided