Vol. 13, No. 1 (2024): Regular Issue

The stabilization of one-dimensional thermoelastic system of full von Kármán beam with a delayed linear frictional damping is considered, where the heat fux is given by Cattaneo's law. Under suitable assumption on the weight of the delay and that of frictional damping, we prove that the system is exponentially stable. The idea here, is to generalize some previous existing results by considering a delayed problem.

Continuum robots have remarkably exceeded rigid robots' abilities for specific tasks, such as the adaptation to twisted paths and their capacity to perform medical surgeries thanks to their flexible structure yet their dynamic modeling are complicated, in particular the highly non-linearity of their equation of motions. To this end, a simplified dynamic model for a variable curvature continuum robot is established and thoroughly developed based on Euler-Lagrange method, namely an approximate formula relating the robot's each unit is integrated in the dynamic model in order to reduce the number of the generated coordinates in the equation of motions. The equation of motions are figured out using Runge-Kutta method through MATLAB environment. To verify the effectiveness of the developed dynamic model, simulation examples through MATLAB are carried out. The first simulation is dedicated to a spatial single section variable curvature continuum robot, in which the robot is initially tilted from its equilibrium position then released and its behavior (oscillation) is graphically represented based on the equation of motions that are solved by Runge-Kutta method. While the second simulation example addresses the behavior of a variable curvature continuum robot when subjected to a force. It is found that the developed dynamic model properly simulates the behavior of variable curvature continuum robots and the Runge Kutta method can be considered as an effective numerical method to deal with the non-linearity of continuum robot's equation of motions.

India is the second most populated country in the world and supply of COVID-19 vaccine is limited. Thus the effective use of COVID-19 vaccine is important. Here we have formulated an age structure SIRS model (Susceptible-infected-recovered- of COVID-19 in India. This model helps us to understand the characteristics of COVID-19 in with and without vaccination scenario. To formulate this model we have considered population factors like contact structure and country specific age structure. Further using optimization algorithm (GA) paired with age stratified mathematical model; we have determined optimal allocation for three matrices-infections, year of life loss, death.We have found that a vaccine with efficacy $\geq 70\%$ would be enough to control death, infection and year of life loss.

An unconditionally stable finite difference scheme is developed and fully analyzed for two-dimensional convection-diffusion-reaction equations with nonlinear coefficients and external sources. The well-known difficulty in obtaining a stable second-order discretization of the convection term is resolved by first adopting a central discretization in space. The semi-discrete convection term is split into the positive and negative parts. Then a non-standard time-integration is proposed - by treating one part implicitly and the other explicitly. This allowed to maintain numerical stability, retain compactness of the stencil and avoid division by the diffusion coefficient, hence can be applied to purely convection (zero diffusion) problems. The solvability, consistency and stability of the scheme are established. Numerical results are provided to verify the theoretical properties.

Simulations are performed to examine the mixed convection flow behavior within a wall-driven square enclosure containing Ag-water nanofluid. The enclosure is assumed to contain a center heater and is acted on by a longitudinal magnetic field. The resulting magnetohydrodynamic (MHD) flow equations are solved using the finite volume method (FVM) and SIMPLE algorithm for two orientations of the heater, namely horizontal and vertical. The simulations focus specifically on the effects of the heater length, Richardson number (Ri = Gr/Re, where 10${}^{2 }$ $\leq$ Gr $\leq$ 10${}^{6}$ and Re = 100), the Hartmann number (0 $\leq$ Ha $\leq$ 100), and the Ag nanoparticle volume fraction (0.0 $\leq$ $\varphi$ $\leq$ 0.09) on the fluid flow and heat transfer performance within the enclosure. It is shown that, irrespective of the heater orientation, the heat transfer rate increases with an increasing heater length. However, as the magnetic field strength increases, the convection effect is suppressed, and hence the heat transfer performance reduces. Also, it is found that heat transfer rate increases with an increasing solid volume fraction of Ag nanoparticles into the pure water.

In this paper, we establish the asymptotic stability and boundedness of the Volterra integro-dynamic matrix Sylvester impulsive system on time scales. First, we convert the linear Volterra integro-dynamic matrix Sylvester impulsive system on time scale to an equivalent Kronecker product Volterra integro-dynamic impulsive system on time scales using vectorization operator. Then, we obtaine the results for asymptotic stability and boundedness of a time-varying Volterra integro-dynamic matrix Sylvester impulsive system on time scales in which the coefficient matrix is not necessarily stable. We generalize to a time scale some known properties concerning the asymptotic stability and boundedness from the continuous version. Finally, we've given some numerical and theoretical examples of the way those advanced analytical consequences may be applied.

This paper presents a survey of research on the study of the impact of different functional responses on prey-predator models in ecology. These functional responses impact the qualitative behaviours of prey-predator models. Further stability and bifurcation analysis of these models are discussed. Graphical representation through numerical simulations are presented.

In this paper, we study a delayed spatio-temporal mathematical model which modeling the spreading of viral infection in the tissues and the activation of virus-specific T lymphocytes with a new explicit virus load function ``bi-phasic and tri-phasic". The model is given in reaction diffusion systems with two delays which represent the local interaction and the propagation of the virus in tissues. The reduced and layer subsystems are studied and we establish that the slow manifold is an attracting one. We prove that the diffusion has no effect on the dynamics of the system, but time delays can modify the dynamics of the system with/without diffusion. Numerical simulations are carried out to illustrate such situations.

Controlling Dengue fever is difficult worldwide due to complex medical management settings. Therefore, such diseases should be diagnosed, and quick-acting control strategies should be used. In this article, the Mathematical Model for the system of differential equations for the spread of Dengue fever is framed and identifies the solutions to control the disease in a short period. The system consists of six equations. The first four equations represent the human population under Susceptible, Infected, Under Treatment and Recovered people (SITR Model). The vector population then comes under the categories of Susceptible and Infected Mosquitoes. In the suggested SITR Model, the identified positivity, bounded solutions, equilibrium points, stability analysis, and reproductive value are all investigated. The research results demonstrate that when the reproduction number is less than or equal to one, it is asymptotically stable (disease-free) and unstable when greater than one. In addition, confirmed a drop in mosquito bite rates, a decrease in the number of people under hospitalization and notification rates, and a rise in cure rates. The simulation on the model of SITR exposed that controlling the route of communication of this disease is necessary if we follow some strategy to restrict the transmission agent and may stop the virus from spreading further in the population.

This paper deals with the Hopf bifurcation direction in a delayed Solow- Verhulst model \cite{Sahbani}. The delay represents the time needed to assess needs for the labor force and the time taken for its recruitment. The direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are derived by applying the normal form method and center manifold theory. We also give numerical examples to motivate the proposal and illustrate our main result.

Power electronic converters have undesirable characteristics that can be influenced by the structure of the converter, the load, the parameters as well as the pulse period, which leads to the malfunction of the converters. For precise positioning tasks, the friction phenomenon plays an important role. In this paper, we first propose to study the dynamics of the general period-1 behavior in a PWM-controlled universal DC motor drive system with nonlinear Coulomb friction and subsequently control the system towards period 1 by optimizing the controller parameters via the particle swarm algorithm (PSO). The dynamic analysis is performed using bifurcation tools, and phase portraits showing that the system exhibits very rich and striking behavior such as periodic orbits, period-doubling bifurcation, quasi-periodicity and chaos control in live mode. In addition, the Filippov method is used to calculate the eigenvalues of the monodromy matrix belonging to the whole system. Finally, the results of the numerical simulation are in almost perfect agreement with the analog results obtained with PSIM. The results obtained in this work have not yet been reported in the literature to the best of the author's knowledge and therefore deserve to be disseminated.

This paper studies the conformable delay differential systems with linear impulses. Firstly, with the help of impulsive delayed exponential matrix function of conformable version and the variation of constants method, we obtain a representation of solutions to homogeneous and non-homogeneous differential equations. Secondly, the existence and uniqueness of solutions to nonlinear conformable impulsive delay differential equations are proved by using Schaefer's fixed-point theorem and Banach fixed-point principle. Finally, an example is given to illustrate our theoretical results.