Nonlinear Analysis: Modelling and Control
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 Scopus (Q2) database since 2009 and in the Web of Science (Q1) database since 2010.
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Stochastic stability of fractional-order quaternion-valued neural networks on time scales with general probabilistic bounded Markovian switching and neutral delays
This paper investigates the stochastic stability problem of fractional-order quaternion-valued neural networks (FOQVNNs) on time scales with general probabilistic bounded Markovian switching and neutral delays. Owing to the noncommutative nature of quaternion algebra and the coexistence of fractional dynamics, time-scale calculus, Markovian switching, and neutral delays, stability analysis becomes highly challenging, especially when conventional decomposition methods are employed. To overcome these difficulties, the considered system is treated directly in the quaternion domain without decomposition, thereby preserving the intrinsic algebraic structure and avoiding unnecessary dimensional expansion. By constructing an appropriate Lyapunov–Krasovskii functional and combining the free-weighting matrix technique with matrix inequality approaches, a sufficient condition guaranteeing stochastic stability for the considered FOQVNNs is derived and expressed as quaternion-valued linear matrix inequalities. The obtained criteria are general and can be efficiently verified by using a numerical example.
Copyright (c) 2026 Cheng Huang | Qiankun Song https://creativecommons.org/licenses/by/4.0
Event-triggered distributed fixed-time optimization for multi-agent system with input time delays over directed networks
This paper develops an event-triggered distributed optimization algorithm (DOA) for directed multi-agent systems. The algorithm is designed to solve fixed-time optimization problems with equality constraints, while also compensating for input time delays. Firstly, the time-delay system is transformed into an equivalent delay-free model by using the method of model order reduction. Secondly, to reduce the consumption of communication resources, an event-triggered communication scheme is utilized. Subsequently, based on Lyapunov stability theory, it is proved that the designed DOA can converge to the optimal solution within a fixed time. Finally, a numerical simulation shows the effectiveness and advantages of the event-triggered DOA for multi-agent systems.
Copyright (c) 2026 Ruiqi Geng | Qiang Zhang | Fei Wang | Ning Li https://creativecommons.org/licenses/by/4.0
Approximate controllability of Caputo fractional Volterra–Fredholm integral equations under nonlocal conditions and impulsive effects
This paper investigates the approximate controllability of a system of fractional control differential equations. The system involves Caputo fractional derivatives, Volterra–Fredholm integral equations, and impulsive effects. The analysis is carried out in the framework of Banach spaces under nonlocal conditions of order r ∈ (1, 2). The main objective is to establish sufficient conditions for the approximate controllability of the proposed control problem. Assuming that the associated linear system is approximately controllable, the analysis relies on tools from fractional calculus, Krasnoselskii’s fixed point theorem, and the theory of resolvent operators. The obtained results extend and improve several existing results in the related literature. Finally, two illustrative examples are presented to demonstrate the applicability of the theoretical findings.
Copyright (c) 2026 Hasanen A. Hammad | Doha A. Kattan | Zhenhai Liu https://creativecommons.org/licenses/by/4.0
Positive solutions to a system of psi-Riemann–Liouville fractional differential equations with coupled boundary conditions
We investigate the existence of positive solutions for a system of ψ-Riemann–Liouville fractional differential equations with positive parameters and sign-changing nonlinearities subject to nonlocal coupled boundary conditions containing Riemann–Stieltjes integrals and fractional derivatives of various orders. To prove our main result, we use the nonlinear alternative of Leray–Schauder type.
Copyright (c) 2026 Alexandru Tudorache | Rodica Luca https://creativecommons.org/licenses/by/4.0
Remetrization techniques for mappings contracting perimeters of triangles
There exists a metric in which a mapping contracting perimeters of triangles becomes a graphic contraction, while the completeness of the underlying space is preserved. The reverse question is also considered. We discuss in which cases those two metrics are equivalent and obtain some stability results of the fixed point problem with respect to the original metric and the induced one. The theory is substantiated with numerous examples and a discussion on the advantages regarding the scope of applications.
Copyright (c) 2026 Marija Ćvetković https://creativecommons.org/licenses/by/4.0
Dynamical analysis of a fractional-order delayed predator–prey system with infected prey
This paper investigates the dynamics and control of a fractional-order delayed predator–prey system with disease in the prey. The existence conditions for all feasible equilibria are analyzed. The local asymptotic stability of these equilibria is then studied by deriving the characteristic equation and establishing the corresponding stability criterion. Furthermore, it is demonstrated that the system undergoes a Hopf bifurcation as the time delay crosses a critical threshold, leading to the emergence of sustained periodic oscillations. To suppress oscillations and control disease transmission, a time-delayed feedback controller is incorporated into the infected prey dynamics. Theoretical analysis reveals that the additional control delay can elevate the critical threshold. Numerical simulations validate this strategy, highlighting its potential for ecological management.
Copyright (c) 2026 Wei Zheng | Jimin Zhang https://creativecommons.org/licenses/by/4.0
A perspective on Banach and Kannan mappings contracting the perimeter of triangles in interpolative metric spaces
This article delves into several well-known mappings within the framework of interpolative metric spaces. To demonstrate the genuine generalization of metric spaces by interpolative metric spaces, various illustrative examples are provided. The properties of mappings that contract the perimeter of triangles are examined, and a necessary and sufficient condition for the existence of fixed points is established for such mappings, supported by relevant examples. Additionally, the study explores generalized Kannan-type mappings and generalizes a fixed point result of metric spaces in the setting of interpolative metric spaces. Further examples are provided in support of our result. Furthermore, an adequate condition for the uniqueness of the fixed points is proposed.
Copyright (c) 2026 Anish Banerjee | Pratikshan Mondal | Lakshmi Kanta Dey | Wutiphol Sintunavarat https://creativecommons.org/licenses/by/4.0
The asymptotic behavior of systemic expected shortfall and marginal expected shortfall under extreme losses
The paper considers the asymptotics of the systemic expected shortfall (SES) and the marginal expected shortfall (MES) in systemic risks. We mainly consider individual losses to be the products of primary variables and random weights, where a dependence structure exists between the primary variable and the corresponding random weight for each loss. When the distributions of the primary variables belong to the intersection of long-tailed and dominatedly varying-tailed distribution function classes, we obtain the asymptotics of SES and MES of individual losses. Particularly, under the coherent capital allocation, more precise estimations for SES and MES of individual losses are presented for the regularly varying-tailed primary variables. Some numerical studies are conducted to check the accuracy of the obtained results.
Copyright (c) 2026 Xiaowen Shen | Kaiyong Wang | Yuan Xie https://creativecommons.org/licenses/by/4.0
Global stability of a double-delay HIV dynamical model with curative mechanism, absorption effect, and Beddington–DeAngelis functional response
This study examines the stability of a modified mathematical model for HIV infection, including two time delays. The novel aspect is that both the absorption effect and the cure rate are incorporated into the model with the Beddington–DeAngelis (BD) functional response. The global asymptotic stability of the infection-free equilibrium and uniform persistence of the model are established. To corroborate the theoretical outcomes, the numerical simulations are illustrated. Numerical simulations reveal how the two time delays, cure rate, and BD functional response influence the eradication of the disease.
Copyright (c) 2026 P. Damith Nilanga Silva | Songbai Guo | B.G. Sampath Aruna Pradeep https://creativecommons.org/licenses/by/4.0
Large-scale performance evaluation of galaxy image classification models trained on small datasets
Many studies have utilized convolutional neural networks to classify galaxies into spiral and elliptical, achieving near-perfect results. However, the authors used relatively small datasets (up to 104,787) that often consist of higher-quality images, making it difficult to extrapolate model large-scale performance. In contrast, we combine data from Galaxy Zoo projects (1, 2, Hubble, CANDELS, DECaLS), preserving as many galaxies as possible. To achieve that, we propose a novel methodology – spiral certainty index (SCI), which allows to extend binary classification by introducing uncertain classes for galaxies where volunteers do not fully agree on the class. Using SCI, we bin galaxies into 2, 3, and 5 classes, resulting in three large datasets of 719,133–800,448 galaxies. We then quantitatively evaluate large-scale performance of Cavanagh, ResNet50, and EfficientNetV2S architecture models by training them using small fractions (0.4–46.5%) of the datasets and validating them on the rest. Experiments were repeated with and without standard augmentations (rotation, flipping, zoom, noise). We conclude that for future research using Galaxy Zoo data, the training dataset of at least 71,913 images (10% of 5-class dataset) is recommended to reach stable accuracy and F1 metrics for all three architectures studied. Below this threshold, Cavanagh, and ResNet50 models either overfit or display high variability of metrics. Moreover, at this threshold or above, the usage of augmentations is equivalent to doubling or even quadrupling (in case of ResNet50 for all classes) the training dataset size. The most stable architecture was EfficientNetV2S, which only overfitted with 2-class dataset, when trained on 3,715 images (0.4% of the dataset), without augmentations.
Copyright (c) 2026 Tomas Mūžas | Andrius Vytautas Misiukas Misiūnas | Tadas Meškauskas https://creativecommons.org/licenses/by/4.0
Fixed point results for four-point Kannan mappings with applications to fractional BVPs and Diophantine equations
In this paper, we introduce and study Kannan-type aggregate pairwise distance mappings defined on four points, formulated through mapping conditions involving the sum of all pairwise distances of a quadrilateral configuration. We analyze their structural properties and clarify their connections with classical Kannan mappings, generalized Kannan-type mappings, as well as with mappings involving the total pairwise distance of a quadrilateral. We further extend the theory by introducing functional generalizations, namely the G-Kannan-type and B-Kannan-type aggregate pairwise distance mappings on four points, in which the constant parameter is replaced by appropriate control functions. Under the assumptions of asymptotic regularity or approximating fixed point sequence, with or without weaker continuity hypotheses, we obtain functional extensions that improve the admissible range of the associated parameters. Finally, applications are provided to the existence of solutions for fractional differential equations with boundary conditions and to a nonlinear Diophantine equation.
Copyright (c) 2026 Ravindra K. Bisht | Stojan Radenović https://creativecommons.org/licenses/by/4.0
Approximate controllability of second-order impulsive integro-differential systems involving state-dependent delay and damping effects via resolvent operator
This paper investigates the controllability of a second-order impulsive damped integrodifferential nonautonomous system with state-dependent delay. The results are established using the properties of resolvent operators related to the second-order system behind them, and the analysis employs key mathematical tools such as Gronwall’s lemma and fixed-point theorems. Assuming the approximate controllability of the corresponding linearized system, we obtain a new set of sufficient conditions developed for the approximate controllability of the nonlinear second-order system. These findings contribute to our understanding of the approximate controllability in complex dynamical systems affected by both damping and state-dependent delay. Finally, we present an application that demonstrates and validates the theoretical findings of this study.
Copyright (c) 2026 Raman Sasikumar | Velusamy Vijayakumar https://creativecommons.org/licenses/by/4.0
Asymptotic synchronization for the inertial neural networks by using the differential inequality skills
This paper explores the asymptotic synchronization (AS) for a class of master-slave inertial neural networks (MSINNs). Without employing the existing study approaches such as matrix measure means (MMMs) and linear matrix inequality (LMI), by planning two classes of novel controllers of the trigonometric functions, two criteria to assure the AS for the considered MSINNs are achieved by utilizing the implicit zero point existence theorem of functions and differential inequality way (DIW). By applying the implicit point existence theorem of functions and constructing the controllers of the trigonometric functions, the more concise and more easily verified results on AS can be obtained for neural networks (NNs) than using LMI and MMMs. Our results reveal that the time delay plays a important part in the AS of the considered networks. Namely, when the time delay is less than a certain constant, the AS between the master system and the slave system can be achieved.
Copyright (c) 2026 Zhibin Dai | Zhengqiu Zhang https://creativecommons.org/licenses/by/4.0
Second-order coupled integral boundary value problems at resonance
This paper investigates the existence of positive solutions for a resonant system of nonlinear differential equations subject to coupled integral boundary conditions involving Riemann–Stieltjes integral. Our analysis is based on Leggett–Williams norm-type theorem for coincidence equations due to O’Regan and Zima. By employing a general abstract framework, we obtain new existence criteria that complement and extend recent results in the literature.
Copyright (c) 2026 Yue Du | Yujun Cui https://creativecommons.org/licenses/by/4.0
Comprehensive bifurcation analysis in a delayed epidemic model with media coverage and asymptomatic infection via fractional PD control
It is well known that both media coverage and the presence of asymptomatic patients have a significant impact on the spread and control of infectious diseases. Therefore, this paper proposes a class of fractional epidemic models that incorporate media coverage and asymptomatic infection. Also, the time delay for individuals’ response to the current media coverage, as well as the time delay of media coverage, are incorporated in our proposed model to make it more practical. Based on fractional proportional-derivative (PD) control method, Hopf bifurcation is investigated by taking the sum of the two time delays and the order of the fractional derivatives as bifurcation parameters, respectively. Some sufficient delayed-induced and order-induced bifurcation conditions are given. The application and effectiveness of the presented theoretical results are illustrated through a simulation example. Furthermore, the impact of the feedback control gains and the media effect weight on the stability and Hopf bifurcation of the considered epidemic model is explored.
Copyright (c) 2026 Yangling Wang | Jinde Cao | Min Xiao | Lingzhi Zhao https://creativecommons.org/licenses/by/4.0
Global asymptotic synchronization for delayed inertial BAM neural networks without controllers via the fundamental solution matrix method
This paper considers the global asymptotic synchronization (GAS) for master-slave delayed inertial bidirectional associative memory (BAM) neural networks (NNs). Most existing studies on GAS rely on the LMI approach, integral inequality, matrix measure, and maximum-valued methods, usually with additional controllers. In contrast, this work achieves GAS without using the above methods or designing any controllers. Instead, two new sufficient conditions are derived via the fundamental solution matrix method for first-order differential systems. For the first time, the fundamental solution matrix method is introduced to deal with the GAS for the NNs.
Copyright (c) 2026 Yiping Shuai | Zhengqiu Zhang | Zhibin Dai https://creativecommons.org/licenses/by/4.0
On the dynamics of the autonomous Duffing–Holmes oscillator
The autonomous Duffing–Holmes oscillator ẋ = y, ẏ = x – x3 + by – kz, ż = w(y – z), depending on the three parameters b, k, and w, has been studied previously by several authors who showed that for certain parameter values, it exhibits chaotic motion, or that numerically it has two periodic orbits coming from a Hopf bifurcation, or that it can have three equilibria for some given values of the parameters. Here we provide new results on the integrability and the global dynamics of the autonomous Duffing–Holmes oscillator using its first integrals and Darboux invariants when these exist for some given values of its parameters.
Copyright (c) 2026 Érika Diz-Pita | Jaume Jaume Llibre | M. Victoria Otero-Espinar https://creativecommons.org/licenses/by/4.0
Volatility is a key measure of financial risk, and GARCH models are widely used to describe its dynamics. However, they do not account for the influence of news sentiment, which can significantly shape market volatility. Recently proposed News-Augmented GARCH model addresses it by incorporating sentiment signals in a nonlinear, asymmetric, and multiplicative form. This paper examines its theoretical properties and performs a simulation-based hyperparameter study. The analysis establishes the existence of a unique and causal solution, derives a stability condition, and evaluates model sensitivity and parameter recovery under controlled scenarios. Results demonstrate robust performance across various settings and provide guidance for informed hyperparameter selection and evaluation, enhancing model’s reliability for empirical applications.
Copyright (c) 2026 Diana Vereškaitė | Jurgita Markevičiūtė | Andrius Buteikis https://creativecommons.org/licenses/by/4.0
Enhanced chaotic maps for sustainable cryptographic security
We propose a comparative study of chaotification techniques that enhance the complexity of one-dimensional maps for sustainable cryptographic applications. Specifically, we examine the use of modulo operation, remainder operation, and k-deep-zoom (k-DZ) transformation applied to the sine map. Each technique’s effectiveness is analyzed using bifurcation diagrams, Lyapunov exponents, and correlation results. Additionally, the statistical performance of the techniques is assessed using the NIST SP 800-22 battery of tests, and the computational efficiency is evaluated in terms of the number of operations. The study aims to identify the best chaotification method for generating robust pseudorandom bit generators (PRBGs) suitable for secure encryption and sustainable cryptography.
Copyright (c) 2026 Nasr-Eddine Mellah | Samir Ladaci | Murilo S. Baptista | Celso Grebogi https://creativecommons.org/licenses/by/4.0
Computational technique for robust dynamic optimization of fractional impulsive switched systems
In this work, we study a robust dynamic optimization problem for nonlinear fractional impulsive switched systems (FISSs) with uncertain parameters. The main novelty lies in directly incorporating parameter sensitivity into the cost functional to enhance robustness against model uncertainty. To solve the resulting problem, the system sensitivity is first computed through an auxiliary FISS, and a time-scaling transformation is employed to reformulate the optimization over fixed switching instants. Tractable gradient expressions are then derived using a set of auxiliary systems. A gradient-based optimization method is subsequently developed to solve the transformed problem together with a numerical scheme tailored for the FISSs. Two numerical examples demonstrate that the proposed technique achieves effective optimization performance and improved robustness.
Copyright (c) 2026 Zhaohua Gong | Benchawan Wiwatanapataphee | Chongyang Liu | Yonghong Wu https://creativecommons.org/licenses/by/4.0
Joint ruin probability and risk contagion measure in a quota-share reinsurance risk model
Consider a quota-share reinsurance risk model with constant premiums and stochastic returns in which an insurer purchases fixed-proportion quota-share reinsurance for its business line. Both the insurer and reinsurer may engage in risk-free investments, with their nonnegative general (not necessarily Lévy) log-price processes following an arbitrary dependence structure. Under the assumption that claim sizes are pairwise strongly quasiasymptotically independent and follow heavy-tailed distributions, this paper derives asymptotic formulas for two types of finite-time joint ruin probabilities and for a risk contagion measure from the insurer to the reinsurer. Furthermore, we conduct numerical studies to verify the accuracy of the derived asymptotic results, using the Monte Carlo method combined with an explicit order-3.0 weak scheme.
Copyright (c) 2026 Yang Yang | Rongshan Huang | Hui Meng https://creativecommons.org/licenses/by/4.0
Positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian
In this paper, we investigate the existence of positive solutions for a fourth-order integral boundary value problem involving impulses and the p-Laplacian operator. First, we construct a linear operator that incorporates impulsive effects, and then analyze its spectral radius properties. Subsequently, under suitable conditions on the spectral radius, we apply the fixed point index theory to establish existence theorems for the problem. Our results cover cases where the nonlinear term exhibits (p – 1)-superlinear/sublinear growth, and the impulsive term satisfies superlinear/sublinear growth conditions.
Copyright (c) 2026 Jiafa Xu | Zhichun Yang | Donal O’Regan | Jiangdong Liao https://creativecommons.org/licenses/by/4.0
Existence of positive solutions for tempered fractional differential equations with p-Laplacian operator
This paper investigates the existence of positive solutions for a specific category of p-Laplacian tempered fractional differential equations in which the nonlinear term f contains an integral operator θ. By employing fixed point theorems for sum operators in partially ordered Banach spaces, together with Krasnosel’skii fixed point theorem, the existence of positive solutions is established. Moreover, iterative sequences are constructed to approximate the unique positive solution of the problem. Finally, three examples are presented to illustrate the main results.
Copyright (c) 2026 Jiqiang Jiang | Minghui Liu | Lishan Liu | Yonghong Wu https://creativecommons.org/licenses/by/4.0
Existence and approximate controllability results for time-fractional stochastic Navier–Stokes equations
This paper deals with time-fractional stochastic Navier–Stokes equations, which are characterized by the coexistence of stochastic noise and a fractional power of the Laplacian. We establish sufficient conditions for the existence and approximate controllability of a unique mild solution to time-fractional stochastic Navier–Stokes equations. Using a fixed point technique, we first demonstrate the existence and uniqueness of a mild solution to the equation under consideration. We then establish approximate controllability results by using the concepts of fractional calculus, semigroup theory, functional analysis, and stochastic analysis.
Copyright (c) 2026 Renu Chaudhary | Simeon Reich | Juan. J. Nieto https://creativecommons.org/licenses/by/4.0
Controllability and Ulam–Hyers stability analysis of conformable fractional differential systems with time delays and impulsive effects
We investigate the controllability and Ulam–Hyers stability of a class of conformable fractional differential systems with time delays and impulsive effects. Specifically, we analyze the movement rules before and after the impulse, utilizing both the Banach and Schauder fixed point theorem to derive controllability. Furthermore, we employ nonlinear functional analysis methods to study Ulam–Hyers stability. To demonstrate the applicability and feasibility of our main conclusions, an illustrative example is provided.
Copyright (c) 2026 Luchao Zhang | Xiping Liu | Mei Jia | Zhensheng Yu | Changxiang He https://creativecommons.org/licenses/by/4.0
Existence, uniqueness and averaging principle for fractional Dirichlet boundary value problems driven by Rosenblatt process and Lévy jumps
We address the existence, uniqueness, and averaging principle for Caputo–Hadamard fractional dynamic systems with Dirichlet boundary conditions driven by Rosenblatt process and pure Lévy jumps. First, Lemma 4 establishes the equivalent integral equation representation of our system. Using this foundation, existence and uniqueness are proved by Banach's contraction principle under stochastic calculus, Lipschitz and finite energy conditions. Subsequently, under appropriate averaging assumptions, the system is averaged out with time scale ϵ. Mean-square convergence between original solution and its counterpart is verified by employing tools such as Wiener–Itô double integral, Cauchy–Schwarz, Doob's martingale, and Gronwall–Bellman inequalities. Eventually, computational example with numerical simulations is provided to support the theoretical results.
Copyright (c) 2026 Jalisraj Arokiyanathan | Ramalingam Udhayakumar https://creativecommons.org/licenses/by/4.0
Fixed-time distributed formation control for nonlinear heterogeneous multiagent systems subject to input nonlinearities and actuator faults
This work focuses on distributed practical fixed-time formation (PFTF) control for heterogeneous multiagent systems (MASs) with inherent nonlinear dynamics, coupled input nonlinearities, and potential actuator faults. Conventional backstepping methods face the challenge of “differential explosion”. To resolve this issue, we propose an innovative command filtering strategy with fixed-time convergence properties, integrated with a compensating mechanism that also ensures fixed-time suppression of filtering errors. Leveraging the synergy of fixed-time control theory, backstepping recursion, and neural networks function approximation, a distributed PFTF control protocol is developed. The designed scheme ensures that the MASs attain the predefined formation configuration within a fixed time, while driving all errors converge to a small residual set. Numerical simulations validate the effectiveness and performance of the proposed approach.
Copyright (c) 2026 Jianmin Jiao | Junmin Li | Chao He | Rui Zhang https://creativecommons.org/licenses/by/4.0
Adaptive fixed-time control with prescribed performance for nonlinear networked control systems under deception attacks
This paper presents a novel fixed-time adaptive control scheme with prescribed performance for nonlinear networked control systems (NCSs) under deception attacks. The Nussbaum function is first employed to tackle the challenge of unknown attack weights and their signs. A hybrid approach integrating a fixed-time performance function with a nonlinear shifting function is used to mitigate the influence of initial conditions on tracking errors. Furthermore, a sufficient condition is derived to guarantee the practical fixed-time stability of NCSs, even in the face of deception attacks. Finally, the effectiveness of the proposed methodology is demonstrated through a mass-spring-damper system simulation.
Copyright (c) 2026 Linfang Shao | Weiwei Sun | Lusong Ding https://creativecommons.org/licenses/by/4.0
Synchronization of quaternion-valued BAM neural networks with time-varying delays
This paper studies the global asymptotic synchronization (GAS) and global exponential synchronization (GES) problems of a class of quaternion-valued bidirectional associative memory neural networks (QVBAMNNs) with time-varying delays. Based on the matrix measure approach and Halanay inequality, sufficient conditions for GAS of unbounded time-varying delay system and GES of bounded time-varying delay system were established. Different from existing methods, this approach does not require the construction of Lyapunov functions and obtains the criteria for system synchronization expressed in terms of norms and measures. Finally, the validity of the proposed theoretical results and the feasibility of the control strategy are verified through numerical simulations.
Copyright (c) 2026 Lu Li | Zhengwen Tu | Tao Peng | Bing Chen | Jiang Xiong | Liangwei Wang https://creativecommons.org/licenses/by/4.0
Evaluation of domain-specific convolutional neural network layers for galaxy classification tasks
Due to increasing amount of data, galaxy image classification is being automated using machine learning, with the most common approach being convolutional neural networks (CNNs). Using domain-specific observations about galaxy morphology, we propose two CNN layers – Focal and Wave. The Focal layer highlights information in the center, while the Wave layer is designed to highlight spiral arms. A comprehensive evaluation of layers is performed using datasets of 4 and 11 (not yet deeply studied) galaxy types, with and without augmentations. With no augmentations, our models outperform best results of models used in other studies with Wilcoxon signed-rank test's p-value of pF1 = 0.002 for both 4 and 11 classes in terms of F1 score (used to better evaluate performance due to inherent class imbalance). Moreover, our layers help reduce overfitting and reliance on augmentation combinations, as our models, despite benefiting less from augmentations, still achieve results comparable to other augmented models. Additionally, our models tuned for 4-class data perform equally well on 11-class data, and vice versa. Finally, an ensemble of our models trained without augmentations achieves comparable results to our augmented models.