Vol. 15, No. 2 (2026): Regular Issue

Modulational instability of a plane-wave mode is known to lead to spontaneous energy localization in nonlinear lattices without the presence of impurities. Where the energy dynamically localizes in the system is highly sensitive to initial conditions. Here we numerically investigate sine-Gordon-type lattices and first show that spatial smoothing of the observed dynamical variables on the lattice can already substantially improve predictions of the eventual localization site from early-time data traces alone, suggesting that the type-III instability that forms the energy hotspot is sensitive to energetic clusters. We then show that machine learning leads to additional dramatic improvement in prediction accuracy. Finally, we also examine the role of chain impurities in determining the localization site.

Smoking is a leading cause of death due to its detrimental effects on various organs, leading to strokes, heart diseases, and other respiratory issues. This paper presents a mathematical model to examine the dynamics of smoking and the recovery rate within a community. The model employs a compartmental approach, consisting of five non-linear differential equations, to analyze these dynamics. Both the local and global stability of the model are investigated. Additionally, the next-generation matrix technique is utilized to perform an in-depth analysis based on the reproduction number $R_0$, which is calculated using Python. Several numerical simulations are conducted to illustrate the findings, highlighting the impact of various parameters on smoking dynamics and the effectiveness of intervention strategies.

Mathematical modeling has become an essential theoretical tool for understanding fundamental aspects of various medical and biological phenomena. This paper develops a mathematical model involving the incomplete $H$-function (I$H$F). The primary objective of this study is to analyze the glucose supply in human blood. The results are comprehensive and emphasize the impact of key parameters on glucose dynamics. These findings uncover intricate relationships between glucose supply and metabolic processes. The model provides a robust framework for exploring scenarios that replicate real-world physiological conditions, highlighting its potential applications in diabetes management and metabolic research.

This article explores a Fredholm-type integral equation featuring an incomplete $\aleph$-function in its kernel, with implications for solving real-world problems representing diverse physical phenomena. Employing fractional calculus and Mellin transform principles, we address an integral problem involving the incomplete $\aleph$-function. The Mellin transform and fractional calculus are subsequently applied to analyze an integral equation using the incomplete $\aleph$-function. Various significant exceptional cases have been identified and scrutinized. The general insights from this article may lead to the formulation of new integral equations and solutions, contributing to the resolution of practical challenges.

This paper studies the bifurcation of limit cycles for a specific predator-prey model called Rosenzweig-MacArthur, that presents persistent oscillations in the amount of individuals of the population from predator group and from the prey group. This model uses a Holling Type II function response. The averaging theory of third order allows to investigate the Hopf bifurcation that exhibits this model, providing an analytical approximation of the bifurcated periodic orbit and its kind of stability.

This paper introduces a new12-term six-dimension, continuous hyperchaotic system derived from the 4D Ma system by merging coupling and linear state feedback control strategies. This system has four positive Lyapunov exponents (LEs) with a non-hyperbolic unstable saddle equilibrium point. It demonstrates various dynamic characteristics, including periodic, quasi-periodic, chaotic, and hyperchaotic. Furthermore, the system is translated into an analog electronic circuit and simulated using an oscilloscope device, showing consistency between MATLAB 2023 and Multisim 14.3 software simulations.

The present study applies functions of new cubic B-splines to compute numerical solutions for the modified time fractional Burgers equation using the $\theta $-weighted scheme, employing time fractional derivative using the Caputo fractional order derivative. The finite difference method is employed for the discretization of time, while the cubic B-splines are used for spatial discretization. The quasi-linearization technique was employed to linearize the nonlinear term in the given fractional differential equation. The effectiveness of the proposed method was tested on one specific problem, with the impact of viscosity $\mu$ and parameter $\beta\in(0,1]$ depicted through 2D and 3D graphs. An algorithm is used to explain the suggested approach, the von Neumann technique was employed to analyze the stability of the suggested scheme, which was found to be unconditionally stable. The second-order convergence of the scheme in both spatial and temporal directions has also been discussed and confirmed. To evaluate the accuracy of the proposed scheme, error norms have been calculated and examined.

This paper explores a novel dual synchronization method for fractional-order complex-valued neural networks (FOCVNN) by combining adaptive control, inequality techniques, and stability theory of fractional calculus. The FOCVNN are separated into two real-valued parts and two imaginary-valued parts. According to the proposed dual synchronization scheme, a chaotic masking method is suggested for encrypting medical images to preserve patient information. Simulation results demonstrate the efficiency of the control laws and parameter updating equations. Additionally, experimental results including histograms, change rate of the number of pixels in the cipher-image (NPCR), unified average changing intensity (UACI), peak signal-to-noise ratio (PSNR) and correlation confirm the effectiveness of the proposed method for secure image communication.

This study investigates the influence of buoyancy force on an unsteady magneto hydrodynamic (MHD) free convection flow oscillating between two inclined plates. The flow is subjected to thermal radiation, chemical reactions, and radiation absorption. The governing equations for the flow, heat, and mass transfer are derived and solved using the perturbation technique and appropriate given boundary conditions. The effects of various physical parameters, such as magnetic field strength, chemical reaction rate, radiation absorption, and plate inclination, on the velocity, temperature, and concentration profiles are analyzed. The results show how buoyancy force significantly influences the flow characteristics and temperature distribution, particularly in the presence of external magnetic fields and thermal radiation. are then graphically examined. Moreover, calculations are made and tabulated data on the rates of heat transmission (Nusselt number) and mass transfer (Sherwood number).

Production of Coffee Arabica in many African countries is challenged by several pests and diseases. Particularly, quantity and quality of coffee production is reduced by coffee berry borer (CBB) and coffee berry disease (CBD). The CBB is a destructive pest caused by Hypothenemus hampei, while CBD is a fungal disease caused by Colletotrichum kahawae. In this study, we focused on developing and analyzing a mathematical model to understand the co-dynamics of CBB and CBD in a coffee plantation ecosystem. The CBB and CBD free and endemic equilibrium point of the model were computed. Mathematically, positivity and boundedness of the solutions, existence of CBB and CBD free and endemic equilibria were investigated. The basic reproduction number is derived using the next-generation matrix. The local and global stability of equilibria are established via Routh Hurwitz-criteria and Lyapunov function, respectively. Finally, the numerical simulations are performed using MATLAB ode45 software to visualize the co-dynamics of the system under various scenarios and validate the analytical results.

In this research, we examine a modified Lotka-Volterra predator-prey model with a square root functional response. We have identified a key result regarding the finite-time extinction of the prey species and provided a comprehensive proof to support this finding. An illustrative example is also included to substantiate our theoretical result. Furthermore, our numerical simulations suggest that the phase portrait exhibits two distinct modes of behavior, where certain positive initial conditions result in convergence toward the predator axis in finite time.

Chickenpox is an acute and rapidly spread infectious disease. In this paper, we examine mathematical modelling and stability analysis of chickenpox disease model in the presence of vaccination in a homogeneous population. The model is structured into eight compartments, which represents the actual structure of chickenpox transmission dynamics. As a result, a nonlinear dynamical system is obtained. In this paper, the vaccinated susceptible individual immediately moves to the recovered class with immunity, while a fraction of the inflow of individuals into the population who are unvaccinated entered the susceptible class and the remaining who are vaccinated move to the immune class. The basic reproduction number of our chickenpox model is determined. A suitable Lyapunov function is constructed for our model, and it is observed that the global asymptotic stability of the disease-free equilibrium depends on the recruitment rate, rate of inflow of individuals that are vaccinated and basic reproduction number of the disease. We found that if all the inflows into the population are vaccinated, the Lyapunov function will be a constant term, which simply means that the population will totally be free from chickenpox infection over time. The global stability of the disease-free equilibrium and the local stability of the endemic equilibrium of the chickenpox model are discussed, in this paper. Using a geometric approach on our seven-dimensional sub-systems, we established the global stability of our chickenpox endemic equilibrium. Some numerical simulations are also carried out in this paper, to determine the role of vaccination and recovery rate in the control and prevention of the spread of chickenpox in a public primary school in a Central City of China. It is found that individual students who are unvaccinated against chickenpox are exposed to higher risk of chickenpox infection at the incubation, prodromal and active stages of the infection periods. We also found that recovery, treatment and vaccination rates played vital roles in the control and prevention of the spread of chickenpox among the school children. We found that vaccination against chickenpox will reduce the spread of the virus up to 90%, which is in line with WHO estimation of 87% to 95%.

This study focuses on investigating the effects of time-periodic thermal modulation on Darcy-Brinkman bio-convection in a porous medium saturated with a Newtonian fluid containing gyrotactic microorganisms. A weak nonlinear stability analysis is performed to analyze the stationary mode of bioconvection with low modulation amplitude. The heat transport measured by the mean Nusselt number, which is governed by a Ginzburg-Landau equation (GLE). The GLE is derived by solvability condition at lowest order of perturbed parameter. The results are presented graphically, illustrating the impact of the system parameters on heat transfer. The results show that both Vadasz number and modulation amplitude have dual effect (either increase or decrease) on heat transfer. On the other hand, an increase in the modified bioconvection Rayleigh number and cell eccentricity leads to a decrease in heat transfer. It is found that only OPM/LBM are effective modulations on heat transfer. This highlights the effectiveness of external modulation to control heat transport in the system. Further, it is found that, the convective heat transfer process may be slow, due to asymmetries and irregularities ($\alpha \neq 0$) of microorganisms than spherical-shaped microorganisms ($\alpha = 0$).

Taeniasis and cysticercosis are recognized as neglected tropical diseases (NTDs) that impact both humans and animals. The pork tapeworm, Taenia solium, is responsible for about $30\%$ of epilepsy cases in endemic areas, and this figure can reach $70\%$ in high-risk communities. Due to the significant disease burden, this research focuses on analyzing the transmission dynamics of these diseases through a deterministic mathematical model. The model integrates human and pig populations, Taenia eggs in the environment, and infected pork. The basic reproduction number, $R_0$, is calculated by applying the next-generation method, revealing that the disease-free equilibrium is stable when $R_0 < 1$, and the endemic equilibrium is stable when $R_0 > 1$. Using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficient (PRCC) techniques, sensitivity analysis is performed to identify the key parameters influencing the infected populations and the reproduction number. The findings indicate that factors such as human infection probability, the rate of shedding by infected individuals, pig slaughtering rates, transmission between pigs, consumption of undercooked pork, pig mortality, the proportion of unconsumed infected pork, and the decay of Taenia eggs in the environment are crucial in driving or controlling the spread of diseases. Based on numerical simulations, several policy recommendations are made, including promoting hygiene and sanitation, inspecting pork meat, ensuring proper cooking, providing sanitation facilities, banning open pig farming, and treating infected individuals to prevent further transmission of taeniasis and cysticercosis.

This paper addresses the security and resource efficiency challenges in networked control systems (NCSs)—specifically, the integer-only operation limitation of homomorphic encryption (HE), ciphertext expansion-induced communication overload, quantization nonlinearities that degrade stability or limit convergence, and the lack of a unified solution integrating security and efficiency. To resolve these issues, a unified encrypted control framework is proposed. For HE's integer constraint, static quantization is designed for control gains and dynamic quantization for system states (adjusting sensitivity by state magnitude to ensure asymptotic convergence of quantized states to equilibrium, overcoming fixed-sensitivity quantizers' bounded stability limitation). Different from traditional encryption control, a quantization-aware dynamic event-triggered mechanism (DETM) is developed to reduce communication load and relieve ciphertext expansion, incorporating quantization-related errors into its triggering condition to transmit encrypted data only when necessary and guarantee Zeno-free operation. Finally, simulation results further prove the proposed method is effective.