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pp. 619-630 | DOI:10.5890/JAND.2024.12.001
Aissa Boukarou, Kaddour Guerbati, Khaled Zennir, Aouatef Mansouri
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In this article, using multi-linear estimate in Bourgain type spaces, we prove the local well-posedness of initial value problem associated with the equation $\partial_{t}w +\partial_{x}^{3}w +\eta(t) \mathcal{L}w+\partial_{x}(w)^{k} = 0,$ $ k=2, 4 $. The solution is established on the line for analytic initial data $u_{0}$ that can be extended as holomorphic functions in a strip around the x-axis. A procedure for constructing a global solution is proposed, which improve earlier results in [1].
pp. 631-642 | DOI:10.5890/JAND.2024.12.002
Rameshbabu Ramar, G. Mohanavel
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In this research paper, a new 3-D chaotic system with infinitely many equilibrium points is introduced and analyzed various basic dynamic behaviors such as dissipativity, stability, Lyapunov exponents, etc. The detailed dynamic analysis of the proposed system is conducted using bifurcation, Lyapunov spectrum, and attractor diagram. It is interestingly noted that the proposed system can generate two-scroll, five-scroll, and a real butterfly-like chaotic attractor which can be used to improve the complexity of the system. Some other interesting features such as total amplitude control and offset boosting control also realized in the proposed system for various engineering applications. The numerical calculation and MATLAB simulation results indicate the rich chaotic dynamics in the proposed system. Furthermore, the adaptive synchronization of the proposed system is achieved with unknown system parameters.
pp. 643-655 | DOI: 10.5890/JAND.2024.12.003
J. Nagaraju, K. Ramesh Babu, M. Pavan Kumar Reddy
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The current investigation addresses the impact of helical force and coriolis effect on linear and nonlinear stability analyses of a couple stress fluid. Normal mode approach is employed to solve the non-dimensional governing equations. The corresponding eigenvalue problem is solved analytically using one-term Galerkin method. The influence of different physical parameters on the system are presented graphically. Ginzburg - Landau equation is derived to analyze the convection heat transport. Helical force parameter has the destabilizing nature on the system. For oscillatory instability, Prandtl number has a destabilizing factor for the system to become unstable. For oscillatory as well as steady instability, the critical thermal Rayleigh number is observed to increase with enhancement in Couple stress parameter and Taylor number.
pp. 657-665 | DOI: 10.5890/JAND.2024.12.004
Rajib Mia
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In this article, we present a comprehensive analytical study to obtain the exact traveling wave solutions to a new formed model of the (2+1)-dimensional BKP equation. We construct exact solutions of the considered model using a recently developed expansion technique. This current proposed technique has been successfully implemented to obtain a few exact solutions of a new formed (2+1)-dimensional BKP equation. In order to understand the physical interpretation of solutions effectively, the 2D and 3D graphs are plotted for each type of the solutions obtained for different particular values of the parameters. Furthermore, it is found that the obtained solutions are periodic and solitary wave solutions.
We anticipate that the proposed method is reliable and can be applied for obtaining wave solutions of the other nonlinear evolution equations (NLEEs).
pp. 667-682 | DOI: 10.5890/JAND.2024.12.005
Yan Liu, Yiming He, He Zhang, Xiaoming Yu, Jianwu Zhou
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In this paper, the dynamics and synchronization characteristics of a single Hindmarsh-Rose neuron and electrical coupling system have been studied. At first, a method for calculating the eigenvalues of the critical point at the discharge state was applied to analyze the bifurcation of the single Hindmarsh-Rose model. Then, the resting state, periodic firing state, and chaotic state under different excitations are obtained. Furthermore, the relationships between the synchronization state and the coupling strength and time delay are investigated in numerical models. The results show that the time lag could cause waveform attenuation and affect synchronization. Finally, circuit models were proposed to simulate the discharge behaviors of neurons. After comparison, the circuit models reproduce some results with acceptable errors. These results can help understand the firing mechanisms and hardware implementation of neurons.
pp. 683-704 | DOI: 10.5890/JAND.2024.12.006
Dethie Dione, Bakary Kone, Mouhamadou Dosso, Tape Grace Esperance
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The dispersion of pollutants in the atmosphere takes place mainly in the atmospheric boundary layer, the most turbulent layer, which is constantly agitated by turbulent movements. This dispersion is influenced by several parameters, such as wind speed and diffusivity, among others. In this paper, we are interested in studying these parameters influencing air pollution, using advection-diffusion equations. This study will first comprise discretizing our different equations by an implicit finite difference method. Then we solve these discretized advection-diffusion equations using an adapted MATLAB program. The results obtained allow us to predict the air quality, which is deduced from the concentration rate of the pollutants in time and space.
pp. 705-722 | DOI: 10.5890/JAND.2024.12.007
Alaa J. Abuiyada, Nabil T. Eldabe, Mohamed Y. Abou-zeid, Sami M. El Shaboury
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The main purpose of this study is to investigate the influence of the chemical reaction and activation energy on peristaltic flow of MHD Jeffery nanofluid through a non-Darcy porous medium in the gap between two coaxial tubes inclined at an angle $\alpha $. Couple stresses, radiation, heat generation/absorption, magnetic field, viscous dissipation, and thermal diffusion and diffusion thermo effects are taken into account. The long wavelength and low Reynolds number approximations are used to simplify the non-linear equations governing the flow. Then, a semi-analytical method called the homotopy perturbation method (HPM) is employed to solve the non-linear equations. Graphs for velocity, temperature, and nanoparticle concentration distributions are plotted. Graphical representations of skin friction coefficient, heat transfer coefficient, Nusselt number, and Sherwood number are sketched. Physical explanations for the results are provided. Findings revealed that the increase of the ratio of relaxation to retardation times of Jeffery nanofluid ${ {\lambda }}_{ {1}}$ and the couple stress coefficient ${\eta }'$ decreases the velocity profile, while the couple stress parameter ${\gamma }_1$ increases it. Also, the velocity has a dual behavior under the infuence of Darcy number $Da$ and Hartman number $M$. Moreover, the temperature decreases with an increase of the radiation parameter $R$, but an opposite reaction observes by increasing Hartman number $M$ and the thermophoresis parameter $Nt$. Furthermore, a reduction in the nanoparticle concentration profile occurs by increasing $ {\xi } $, ${\rho }_1$, and $ {E}$. The motion of gastric juice when an endoscope is inserted through a small intestine is a famous example that describes the model of this study.
pp. 723-734 | DOI: 10.5890/JAND.2024.12.008
K. Ramkumar, S. Varshini, K. Banupriya, K. Ravikumar
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The objective of this paper is to investigate the existence and stability results of second-order neutral stochastic functional differential equations with random impulses in Hilbert space. Initially, we establish the existence results of mild solutions of the aforementioned system using Banach Contraction Principle. The results are formulated using stochastic analysis techniques. In the later part we investigate the stability results through continuous dependence of solutions on initial conditions.
pp. 735-760 | DOI: 10.5890/JAND.2024.12.009
Yasmeen M. Mohamed, Nabil T. M. El-Dabe, Mohamed Y. Abou-Zeid, Doaa R. Mostapha, Mahmoud E. Oauf
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The present analytical study exposed the impact of Cattaneo -- Christov heat and mass fluxes on the peristaltic blood influx. The impacts of Hall and ion slip currents are imposed. The Sisko micropolar nanofluid through porous midst is also presumed. The influences of heat generation absorption, thermal radiation, and chemical reaction are presupposed. The slip constraint for both velocity and temperature are postulated. The convective restrictions for nanofluid volume fraction and concentration are examined. The coupled differential systems of equations yield Soret and Dufour feature. The supposition of the long wavelength as well as low Reynolds number is applied to convert the system of partial differential equations into an unpretentious formula (ordinary differential ones). Over and above, the resultant analytical solutions of these equations are tackled essentially by employing both procedures of the conventional perturbation and the homotopy perturbation method (HPM). The diverse physical variables impact on the resultant allocations are calculated numerically and elucidated graphically through a group of graphs. It is recorded that the axial velocity dwindles with an escalating in the magnitudes of Hartman number. Meanwhile, it elevates with rising in Sisko parameter. The spin velocity decays with the elevating in the microrotation parameter. The enriching in heat relaxation causes a dwindling influence on the temperature. Further, escalating the nano Biot number causes a declination in nanoparticles volume fraction. This study is very helpful and has prosperous significant in diverse medical implementations as gold nanoparticles are utilized in the remedy of cancer tumor.
pp. 761-780 | DOI: 10.5890/JAND.2024.12.010
Bikash Kumar, Manoranjan K Singh, Debnarayan Khatua, Anupam De
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The World Health Organization announced worldwide hepatitis C virus (HCV) eradication goals in 2016, including an 80\% decrease in HCV transmission by 2030. People who inject the drug (PWID) are responsible for most of the new HCV infections.Hence, elimination initiatives must pay special attention to this group. Mathematical modeling can provide important information on the level and goals of intervention, which is urgently needed because governments seek guidance to eliminate PWID. A thorough assessment of the state of the mathematical modelling of hepatitis C virus (HCV) infection is given in this article. The article starts by reviewing HCV's fundamental biology and the difficulties in understanding the virus. The paper then focuses on the numerous mathematical models created to investigate various facets of HCV infection, such as viral dynamics, host-virus interactions, and therapeutic results. The review also discusses the most recent developments in systems biology and how they relate to the investigation of HCV. The study provides important insights into the dynamics of HCV-HIV coinfection and highlights the need for integrated approaches to prevent and manage the two infections. Mathematical modelling allows the analysis to simulate complex biological systems and predict disease. The focus on HCV-HIV coinfection provides a valuable perspective on the interplay between the two viruses. The article's conclusion discusses the possible advantages of a multidisciplinary approach for comprehending the intricate interactions between the virus and the host and future opportunities for mathematical modelling of HCV.
pp. 781-793 | DOI: 10.5890/JAND.2024.12.011
Ali Sadik Gafer Qanber, Omar Imad Shukri Windi
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Based on the Hertz's nonlinear contact law, the purpose of this article is to analyze the theory of low-velocity impact (LVI) on a functionally graded (FG) viscoelastic plate. CNTs are used as a plate reinforcement and Poly (methyl methacrylate) is used as a matrix. Considering the size factor, CNTs are distributed along the thickness of the plate with different functions, including uniform (UD) and FG states. Considering the viscoelastic coefficient, the relationship between the stress and strain is rewritten. To obtain the motion equations of the forced vibrations caused by the impact, the first-order shear deformation theory (FSDT) of the plate and the kinetic and strain energies of the impactor and plate assembly are written. Finally, a set of mass, damping and stiffness matrices are provided. The effect of changes in the viscoelastic coefficient is investigated for the case that the distribution of CNTs includes states UD, FGV and FGX, and also the CNTs volume fraction includes values of 0.12, 0.17, and 0.28. For this purpose, the responses of impact force and plate center deflection are studied. The results show that the effect of changes in the viscoelastic coefficient is more focused on plate center deflection and the contact force did not change much. In other words, with the increase of viscoelastic coefficient, the maximum value of plate center deflection is decreased.
pp. 795-803 | DOI: 10.5890/JAND.2024.12.012
Evandro G. Seifert, Jose Trobia, Fatima E. Cruziniani, Diogo L. M. de Souza, Elaheh Sayari, Enrique C. Gabrick, Kelly C. Iarosz, Jose D. Szezech Jr, Ibere L. Caldas, Antonio M. Batista
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Insulin is a hormone that plays a crucial role in regulating the blood
glucose. It is secreted by the beta cells of the pancreas. A chronic disease,
known as diabetes, occurs when there is no effective use or no enough secretion
of insulin. The treatment, such as insulin injections and medicines, depends on
the type of diabetes. Mathematical models have been proposed to understand
the dynamics of the glucose-insulin regulatory system in different conditions.
In this work, we investigate a model that describes the dynamics of the
glucose and insulin concentrations with beta cells. We introduce the effect of
medication in a glucose-insulin model. It is analysed a treatment with
continuous medication and another with discontinuity in the drug use. We
identify parameter values related to medicines that maintain the blood glucose
concentration in a normal level.
pp. 805-821 | DOI: 10.5890/JAND.2024.12.013
Zhiyi Jing, Yeyin Xu, Qiang Fan,Ying Wu
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Information flow in a brain functional network has significant effects on the causality between brain regions and emotion generation. Investigation of such causal relationships under different emotional states is key to reveal the emotion generation mechanisms. In this research, the dynamic directed networks are constructed by transfer entropy method based on DEAP electroencephalogram emotion data set. The information exchanging of the brain network is captured in short-term time scales. The functional separation and integration ability of brain, information flow and robustness of the network in different emotion states are analyzed.
The results found that in the high arousal-high valence and low arousal-high valence states, information separation and integration ability became stronger and the robustness turned high. In the same emotional states, the information flow of the brain regions at all directions varied synchronously. Kinds of machine learning methods combined with the characteristics of the dynamic network are adopted to conduct emotion recognition of testees. Compared with the results of different classifiers in emotion recognition, the classifier built by support vector machine had a higher accuracy. With the accuracy of 96.9\% of subject-dependent two-classification, a high precision classifier is successfully achieved in the research which provides an effective method for the future investigation on emotion classification and recognition.
pp. 823-833 | DOI: 10.5890/JAND.2024.12.014
Yu-Qian Chen, Hao Si, Xiao-Juan Sun
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It has been shown that both periodic pulse packets and single pulse packet can be propagated in feedforward neuronal networks by including resonance pair. Based on these results, we further study the selective propagation of pulse packets in such feedforward neuronal networks. The obtained results show that periodic pulse packets can be propagated selectively when their periods match the network frequency, which can be controlled by background input, connection strength, and intra-layer connection probability. The relationship between these control parameters and network frequencies suggests that neuronal networks may adaptively change their states by modulating some parameters in order to selectively propagate signals.
pp. 835-846 | DOI: 10.5890/JAND.2024.12.015
L. C. Vestal, Z. E. Musielak
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The abundance of gauge functions in dynamics is compelling because
the total derivative of any scalar function can become a null Lagrangian,
which makes the Euler-Lagrange equation identically zero. Thus,
gauge functions have no direct effects on the resulting equations of
motion. However, there is a special family of gauge functions that can
be related directly to forces and nonlinearities in dynamical systems
by using a method developed in this paper. To identify this special
family, general gauge functions are constructed for second-order
ordinary differential equations of motion describing one-dimensional
dynamical systems. The gauge functions corresponding to forces and
nonlinearities in a variety of known oscillators, including the Duffing
oscillator, are presented, and the novel roles these functions play in
classical dynamics are discussed.
