Nonlinear Engineering

Abstract A forward start option is an exotic option with delayed activation and reduced premium that allows investors to avail market opportunities in the future. Moreover, mean-reversion explores the investment strategies. This study examines the pricing of forward start options based on the uncertain mean-reverting stock model by applying Liu’s uncertain finance. Call and put options pricing formulas are derived. The study depicts that the pricing patterns in uncertain environments are consistent with the common characteristics of financial markets.

Muhammad Shoaib Khan

Javed Hussain

Tareq Saeed

Valuation of forward start option with mean reverting stock model for uncertain markets

不确定市场中均值回归股票模型的远期启动期权估值

Abstract In response to the shortcomings of insufficient efficiency in calculating geometric nonlinear features and high environmental impact in the current construction, this study explores the control of nonlinear geometric structures based on an updated Lagrangian model function in the construction. In this method, the change in the geometric nonlinear stiffness is analyzed using generalized stiffness parameters and a displacement increment method, and the iteration step size and loading/unloading directions are adjusted in the iteration process to achieve the convergence of the solution. In the simulation experiment, the proposed method took 126 s to calculate the incremental iteration steps 700 times in a conventional environment, which is 28.8% more efficient than the cross-sectional method. In the simulated disaster environment, the model took 1,615 s to calculate the ultimate load of 84 contact elements, which is 43.1% more efficient than the section method and 62.6% more efficient than the discrete analysis method. Experimental results showed that the displacement judgment calculation efficiency of the method proposed in this study is higher than that of other models under different loading and unloading conditions and even in geological disaster states. This method had high environmental adaptability in solving nonlinear building structures and could improve the efficiency of solving general nonlinear building results.

Ling Li

Geometric nonlinear analysis based on the generalized displacement control method and orthogonal iteration

基于广义位移控制方法和正交迭代的非线性几何分析

Abstract The synchronization of chaotic systems has garnered considerable attention across various fields, including neuroscience and physics. Particularly in these domains, synchronizing physical systems such as laser models is crucial for secure and rapid information transmission. Consequently, numerous studies investigate the synchronizability of different laser networks by establishing logical network frameworks. In this study, we employed a minimal universal laser (MUL) model designed to capture the essential dynamics of an actual laser model within just three dimensions. Within the network model of MUL systems, we introduced the linear diffusive function of neighboring nodes’ fast variables into the feedback term of the lasers, with models arranged in a global network structure. Our examination of synchronization within the constructed MUL network utilized master stability functions and the time-averaged synchronization error index. The findings suggest that while the network fails to achieve complete synchrony, it exhibits various synchronization phenomena, including cluster synchronization, chimera states, extreme events, and multistability. These results shed light on the complex dynamics underlying the synchronization of chaotic systems in networked environments, offering insights relevant to numerous applications across diverse fields.

Mahtab Mehrabbeik

Fatemeh Parastesh

Karthikeyan Rajagopal

Sajad Jafari

Matjaz Perc

Riccardo Meucci

Minimal universal laser network model: Synchronization, extreme events, and multistability

极简通用激光网络模型：同步、极端事件与多稳态

Abstract Shallow water waves represent a significant and extensively employed wave type in coastal regions. The unconventional bidirectional transmission of extended waves across shallow water is elucidated through nonlinear fractional partial differential equations, specifically the space–time fractional-coupled Whitham–Broer–Kaup equation. The application of two distinct analytical methods, namely, the generalized logistic equation approach and unified approach, is employed to construct various solutions such as bright solitons, singular solitary waves, kink solitons, and dark solitons for the proposed equation. The physical behavior of calculated results is graphically represented through density, two- and three-dimensional plots. The obtained solutions could have significant implications across a range of fields including plasma physics, biology, quantum computing, fluid dynamics, optics, communication technology, hydrodynamics, environmental sciences, and ocean engineering. Furthermore, the qualitative assessment of the unperturbed planar system is conducted through the utilization of bifurcation theory. Subsequently, the model undergoes the introduction of an outward force with the aim of inducing disruption, resulting in the emergence of a perturbed dynamical system. The detection of chaotic trajectory in the perturbed system is accomplished through the utilization of a variety of tools designed for chaos detection. The execution of the Runge–Kutta method is employed to assess the sensitivity of the examined model. The results obtained serve to underscore the effectiveness and applicability of the proposed methodologies for the assessment of soliton structures within a broad spectrum of nonlinear models.

Muhammad Bilal Riaz

Adil Jhangeer

Jan Martinovic

Syeda Sarwat Kazmi

Bifurcation and chaos: Unraveling soliton solutions in a couple fractional-order nonlinear evolution equation

分岔与混沌：揭示一对分数阶非线性演化方程中的孤子解

Abstract Hepatitis B, a liver disease caused by the hepatitis B virus (HBV), poses a significant public health burden. The virus spreads through the exchange of bodily fluids between infected and susceptible individuals. Hepatitis B is a complex health challenge for individuals. In this research, we propose a nonlinear HBV mathematical model comprising seven compartments: susceptible, latent, acutely infected, chronically infected, carrier, recovered, and vaccinated individuals. Our model investigates the dynamics of HBV transmission and the impact of vaccination on disease control. Using the next-generation matrix approach, we derive the basic reproduction number <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msub> <m:mrow> <m:mi>R</m:mi> </m:mrow> <m:mrow> <m:mn>0</m:mn> </m:mrow> </m:msub> </m:math> {R}_{0} and determine the disease-free equilibrium points. We establish the global and local stability of the model using the Lyapunov function. The model is numerically solved using the higher-order Galerkin time discretization technique, and a comprehensive sensitivity analysis is carried out to investigate the impact of all physical parameters involved in the proposed nonlinear HBV mathematical model. A comparison was made of the accuracy and dependability with the findings produced using the Runge–Kutta fourth-order (RK4) approach. The findings highlight the critical need for vaccination, particularly among the exposed class, to facilitate rapid recovery and mitigate the spread of HBV. The results of this study provide valuable insights for public health policymakers and inform strategies for hepatitis B control and elimination.

None Attaullah

Salah Boulaaras

Aasim Ullah Jan

Tahir Hassan

Taha Radwan

Mathematical modeling and computational analysis of hepatitis B virus transmission using the higher-order Galerkin scheme

利用高阶Galerkin方法的乙型肝炎病毒传播的数学建模与计算分析

Abbreviation
Journal Impact	2.22
Quartiles(Global)	MATHEMATICS, INTERDISCIPLINARY APPLICATIONS(Q2)

ISSN	2192-8010, 2192-8029
h-index	30

Publication Information	Publisher: Walter de Gruyter GmbH，Publishing cycle: ，Journal Type: journal，Open Access Journals: Yes
Basic data	Year of publication: 2012，Proportion of original research papers: 100.00%，Self Citation Rate:4.20%， Gold OA Rate: 96.15%
Journal Fees	$Details
Average review cycle	44 weeks

Nonlinear Engineering

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Valuation of forward start option with mean reverting stock model for uncertain markets

Geometric nonlinear analysis based on the generalized displacement control method and orthogonal iteration

Minimal universal laser network model: Synchronization, extreme events, and multistability

Bifurcation and chaos: Unraveling soliton solutions in a couple fractional-order nonlinear evolution equation

Mathematical modeling and computational analysis of hepatitis B virus transmission using the higher-order Galerkin scheme

Valuation of forward start option with mean reverting stock model for uncertain markets

Geometric nonlinear analysis based on the generalized displacement control method and orthogonal iteration

Minimal universal laser network model: Synchronization, extreme events, and multistability

Bifurcation and chaos: Unraveling soliton solutions in a couple fractional-order nonlinear evolution equation

Mathematical modeling and computational analysis of hepatitis B virus transmission using the higher-order Galerkin scheme