Vol. 14, No. 1 (2025): Regular Issue

This study investigates the flow characteristics of a nanofluid composed of nickel zinc ferrite $(NiZnFe_2O_4)$ and SAE 20W40 motor oil (Society of Automotive Engineers) within a porous medium while optimizing entropy on a stretchable sheet. Such simulations play a crucial role in assessing cooling or heating rates at electromagnetic interfaces, industrial equipment (like cooling turbine blades and combustion systems), orthopedic joint replacements, aircraft turbines, bone plates, and tumor treatments. Irreversibility analysis is developed, considering factors like partial slip, melting, and viscous dissipation to scrutinize various properties of the nanofluid flow. The nanoparticle volume fraction characterizes the nanofluid's behavior. A spectral local linearization method is employed to solve the highly nonlinear ODEs (Ordinary Differential Equations) resulting from Lie group analysis. The study explores the effects of relevant parameters on streamline visualization and physical quantities (surface friction, heat transmission rate, entropy generation, and Bejan number), validating them against existing literature. Results indicate that higher volume fractions lead to reduced friction, the melting parameter helps to increase heat transmission (by $37.98\%$) and reduce entropy (by 61.72%).

The nonlinear and linear approach, as well as a fully nonlinear energy argument, are used to thoroughly examine the thermal convection of simultaneously rotating Navier-Stokes-Voigt fluid for three distinct bounding surfaces. It is observed that the same critical Rayleigh number is obtained using both nonlinear and linear analyses, which ensures the absence of sub-critical instability. A nonlinear energy argument describes the important role of the Kelvin-Voigt parameter in energy decay, whereas the parameter doesn't affect the value of the Rayleigh number. The vertical fluid motion slows down due to rotation; thus, rotation postpones the onset of instability. Also, discussed the stability of Navier-Stokes-Voigt fluid contained in three different combinations of bounding surfaces.

Through the development of a mathematical model, the impacts of predator harvesting in the presence of infectious prey are examined. It is commonly established that only harvesting or only infectious disease may cause species extinction. In contrast the combined effects of harvesting and infectious disease on species extinction in an eco-epidemic system was unexplored. In order to examine various dynamical circumstances, various predator harvesting strategies are included in this paper. The essential theoretical properties of the models such as dissipativity, local and global stability analysis of equilibrium points are done. The Hopf bifurcations and its continuations are evaluated with the variation of ecological parameters. The maximum sustainable yields are determined with the variation of harvesting effort. Numerical results of the system dynamics and bifurcation analysis are presented for experimentally obtained parameter values. The key observation is that uncontrolled harvesting of predator species not only cause predator extinction but also it may led to rapid extinction of prey species. The study's conclusion is that, in real-world eco-epidemic systems, the combined impacts of predation in the presence of infection in the prey can accelerate the extinction of prey species compared to the case of predation simply in the absence of infection.

In this paper, we investigate a modified (2+1)-dimensional Ablowitz-Kaup-Newell-Segur (mAKNS) water wave equation. The method of symmetry analysis will be employed to find exact solutions of the mAKNS equation. In addition, we will implement the method of the multiplier approach to search for the admitted conserved vectors of this equation. Furthermore, a physical interpretation showing solution wave structures, density plots and wave propagation will be presented. The results obtained can be used to investigate further interaction of water waves in a variety of localized structures and high-dimensional models in other areas of nonlinear science.

The aim of this work is to propose and investigate the global stability of a delayed SEIR epidemic model with a generalized incidence function. The proposed model also includes general treatment function and vaccination term. Using the Lyapunov functions in the absence of delay, we show that the disease-free steady state is globally asymptotically stable if $R_{0} \leq 1$, and the disease-endemic steady state is globally asymptotically stable if $R_{0} > 1$, where $R_{0}$ is the basic reproduction number. For specific functions which are given to the treatment function and the incidence function, we show that the vaccination and early treatment play an important role in healing. Moreover, numerical simulations are given to illustrate and confirm our main analytical results.

The predator-prey system with additive Allee effect in the growth rate of prey is proposed and studied. The proposed system is extended by introducing hyperbolic mortality rate for top predator instead of using common linear mortality rate. The system is analysed in terms of both analytical and numerical aspects. The model system demonstrates that when the system's parameters are changed, it exhibits both stable and unstable dynamics. The Hopf point bifurcation is also studied in the proposed system. The study enhances dependence of the system's dynamics on Allee effect and other crucial parameters. The discipline of forestry and natural ecology can benefit from the findings and experience gained from this study.

In this paper, we consider a SEIR epidemic model in which recruitment is assumed to be governed by a logistic function. Mathematical analysis is used to study the dynamic behavior of this model. A threshold parameter $R_0$ is identified which governs the spread of disease, and this parameter is known as the basic reproduction number. The model has at least three equilibria, one endemic equilibrium and two disease-free equilibria. We demonstrate that the first disease-free equilibrium is always unstable and that the second disease-free equilibrium is locally asymptotically stable when the basic reproduction number $R_0$ is strictly less than unity. Otherwise, when the $R_0>1$ and by choosing the intrinsic growth rate of the population $r$ as bifurcation parameter, we show that the system loses its stability and a Hopf bifurcation occurs. Next, trying to validate the SEIR model and estimate the parameters that minimize the error between the numerical simulations and the real experimental data, we have determine the inverse problem associated with identification and we solved it. The resulting calibrated model has parameters and returns reasonable predictions that better represent reality. Furthermore, a backtracking design is proposed to achieve stabilization of the SEIR model towards the second disease-free equilibrium point. The proposed method is a recursive scheme based on Lyapunov and provides a systematic procedure to design stabilizing controllers. The proposed controller extinguishes disease and stabilizes the chaotic motion of the system using a single control input. Finally, numerical simulations that illustrate each part of this work are represented.

In biological neuronal systems, information propagation and processing are based on signal detection. Stochastic resonance (SR) is an universal phenonmenon for detecting information in nonlinear dynamic systems. In this paper, we investigate the influence of coupling strength from inhibitory neurons on stochastic resonance (SR) in small-world neuronal networks. Each neuron is described as FitzHugh-Nagumo (FHN) model. The main results report that multiple optimal noise could induce stochastic resonance (SR), which is referred as stochastic multiresonance(SMR), and inhibitory neurons could either destroy stochastic multiresonance(SMR) or turn stochastic multiresonance(SMR) to stochastic resonance(SR) in neuronal network.

The problem of dust acoustic dressed solitons is addressed in an unmagnetized collisionless dusty plasma with ions satisfying a $\kappa$-distribution. The approach based on the expanding of the Sagdeev potential up to the fourth-order has been generalized to the non-Maxwellian dusty plasma. This approach yields a second order inhomogeneous differential equation termed dressed soliton. The resulting dressed soliton is then expressed as a sum of the usual K-dV solution and the higher-order nonlinearity terms. The range of main parameters ($\kappa$ and $\lambda$) where the higher order correction is valid is explored. In particular, the suprathermal parameter values required to the valid dressed solitons are shifted toward higher values as the velocity $\lambda$ increases. Furthermore, our numerical investigations reveal that the main quantities of all localized structures are significantly modified by the suprathermal effects. Our results should help in providing a good fit between theoretical and experimental results.

In this paper we obtain novell solutions of the modified Kortweg-de Vries- Zakharov-Kuznetsov equation by employing the Lie group analysis and the $(G'/G)$-expansion method. The solutions to be obtained are solitary wave, perodic and rational solutions. Utilizing the Lie group analysis, the the modified Kortweg-de Vries- Zakharov-Kuznetsov equation is integrated. The Lie symmetry technique is distinct from the conventional integrability approaches, which also include Hirota's bilinear method and the multiple exp-function method, among others. The solutions capture the limiting behavior of problems that are far from their intial or boundary conditions. The conservation laws for the underlying equation are also derived by using the multiplier method. The precise solutions provided in this work are anticipated to act as a starting point for numerical simulations of the underlying equation. Furthermore we intend to construct further physical solutions of interest by employing the conservation laws reported here in this paper and these results will be reported elsewhere.

In the present paper, we consider a special family of equations that are known to incorporate important wave features in oceanography studies. Physically, these equations admit generalized symmetries and non constant separants which implies they are of great relevance to integrability studies. These equations, are highly nonlinear and once reduced, are not solvable by conventional techniques. We construct series to effectively solve these evolution equations wherein recurrence relations occur and the convergence may be tested. Moreover, the conserved vectors of the equations are established.

The aim of this numerical simulation is to investigate the heat and mass transfer on mixed convection nanofluid flow over a vertical wedge with double dispersion, thermophoresis and Brownian motion. Non-similarity transformations are used to transform the continuum equations which govern the flow in to dimensionless form and the obtained ordinary differential equations are evaluated using Shooting with Runge Kutta 4th order. The emerging parameters such as $D_f$ and $D_s$ - Solutal and thermal, $N_r$ -Buoyancy ratio, $N_t$ -Thermophoresis, $N_b$ -Brownian motion, and $m$ -wedge angle impacts on coefficients of heat and mass transfer, Concentration, Temperature, and Velocity are demonstrated through tables and graphs. The coefficient of heat and mass transfer amplifies with amplification in $m$. The outcome of the current investigation is accurate when compared with existing work. The present article is suitable to the solutal and thermal flow of nanomaterials processing in environmental engineer-ing, the chemical industry, and food technology.

Resonant behavior of two 3-DOF systems with a limited power supply (or so-called non-ideal systems) is analyzed. Resonant steady states are constructed by the multiple scales method. Transient is presented using the two-points Padé approximants containing exponents. Obtained analytical results are compared with a numerical simulation. It is shown that amplitudes of the resonance vibrations of the elastic sub-system can be essentially decreased by change of the system parameters.

The couple system of nonlinear partial differential equation under investigation base on extension of modified rational expansion method. In this article, with the help of symbolic computation Mathematica successfully constructed the various kinds of solitary wave solutions named anti-kink soliton, travelling wave solutions, bright soliton, kink soliton, dark soliton, kink dark solitons, kink bright solitons, anti-kink dark solitons, and anti-kink bright solitons for nonlinear Whitham-Broer-Kaup equation. The calculated results are very interested, different and novel which have not been investigated in past studies. The graphical demonstration of constructed solutions demonstrate by 3-D, 2-D, contour shape by computer software Mathematica. The investigated results will be play keen role in the study of nonlinear physical phenomena in nonlinear sciences and constructed results prove that EMRE approach is very efficient, reliable, powerful for the investigation of other nonlinear partial differential equations.

Nonlinear heartbeating dynamics have become a hot issue nowadays. More and more attention has been drawn on the nonlinearity of the heartbeating models. Previous studies adopted numerical integration method and cared more about the single solutions or time-series results. Based on a discrete mapping method, this study deals with the semi-analytical solutions and stability of a heartbeating model consisted of coupled van der Pol oscillators. The heartbeating model is discretized to form implicit mappings by a midpoint scheme. Nonlinear firing characteristics varying with the excitation frequency, such as stability and bifurcation, are predicted by eigenvalue analysis. Stable and unstable heartbeating waveforms are illustrated through bifurcation and phase diagram to provide dynamic information for situation where arrhythmia may occur. Global and independent firing waveforms are discovered and distinguished in the study. Independent period-2 and 3 firing waveforms are solitary and limited by saddle node bifurcations. The results, especially the period-doubling bifurcations and the unstable action potential waveforms obtained based on the discrete mapping method, can be referred in clinical treatment.