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

The dynamical model for a dynamical system might change during its full life cycle, and it is important to update the corresponding model during such a system is on duty. In this paper, a Filippov-type discontinuous dynamical system which is consisted with multiple sub-systems is investigated. The switching functions for such a discontinuous dynamical system switching from one sub-system to another, as well as the system parameters of the sub-systems are considered to be time-varying. When such a Filippov-type discontinuous dynamical system is governed by one of the sub-systems, the actual excitations including internal and external forces will be evaluated through super-twisting sliding mode observer and recursive least squares in case of inaccurate sub-system modeling and system parameters variation. The event-triggered technique will be adopted to identify the change of the switching functions, and a novel method to updating the switching functions will be designed. The generalized equations of such a self-updating approach will be provided for such a Filippov-type discontinuous dynamical model, which can be further extended to build the confidential digital twin model.

This work presents an analytical approach to analyze the hydroelastic behavior of floating membrane breakwater under the assumption of linear shallow water theory. The analysis is carried out by assuming that the membrane bottom surface is at the water's surface and the transverse vibration of the membrane is seen as a wave propagating over the membrane breakwater. The solution to the associated problem is obtained by matching the wave propagation in the membrane to the wave propagation at the bottom of the membrane surface. It is seen that the amplitude of the deflection of the membrane decreases with an increase in the tensile force.

Present numerical analysis describes the impact of thermal and solutal stratifications on the boundary layer flow of magnetized second-grade fluid over an exponentially stretching sheet under the influence of viscous dissipation and porous medium effects. The doubly stratified porous medium comprised with a stretchable sheet of the form $U_w(x)= U_oe^{{x}/{L}}$ and designated along the axial flow direction with $T_w(x)= T_o+be^{{x}/{2L}}$ and $C_w(x)= T_o+ae^{{x}/{2L}}$ is the thermal and concentration fields at the surface. Based on the flow geometry, the current physical situation yields the complex nonlinear system of differential equations and which are not amenable to any of the direct methods. Hence, a robust Runge-Kutta 4$^{th}$ order method is implemented to solve the representative system of flow equations. The outcomes of the current investigation are presented for various values of physical parameters in the boundary layer regime adjacent to the stretching sheet in the form of velocity, thermal and concentration profiles. Momentum boundary layer thickens and thermal profile significantly suppressed for the enhancing values of second-grade fluid parameter. Adjacent to the stretching sheet, the velocity field considerably diminished for the rising values of magnetic number. Magnifying Brownian motion parameter suppressed the concentration field, whereas increasing thermophoresis parameter enhances the concentration field. Thermal and concentration fields significantly decayed for the increasing values of thermal and solutal stratification numbers. However, the similarity solutions presented in this investigation excellently matching with the former results in the literature and this fact assures the validity of the current solutions.

The present study considers the dynamical response of an eco-epidemiological model consisting of prey and infected predator species population. Here, Leslie–Gower type model is considered for predator–prey interaction where the most common mathematical form to express the Allee effect in the prey growth function is considered. The well-posedness, existence and stability of different equilibria were explored thoroughly. Each equilibrium is stable both locally and globally within some prescribed regions and parametric condition. Hopf bifurcation around the interion equilibrium is explored and Allee threshold plays a significant role as bifurcation parameter. Suitable set of parameter values were observed for which transcritical bifurcation is observed around the boundary equilibrium point. Our analytical findings are exemplified through computer simulation using MATLAB, which show that this model may be valuable for analysing the ecological and eco-epidemiological phenomena in our eco-system.

Mathematics has many applications in other sciences, especially in chemistry, where the theory of chemical graphs is one of the most important uses. Analyzing the properties dependent on the structure of different molecules is of significant importance. One of these molecules, whose structure is investigated in this article, is Bismuth tri-iodide [m, n]. In this article, we investigate the relations between the first $\delta$- Gourava index, second $\delta$- Gourava index, SK Revan index, SK1 Revan index, and SK2 Revan index via M-polynomials. These indices are then calculated for the molecular graph and the line graph of Bismuth tri-iodide [m, n], and the results are presented.

In this paper, the applications of the Yang transformation technique are considered to deal with the non-linear fractional Korteweg-de Vries (KdV) equation and fractional coupled Korteweg-de Vries (CKdV) equation. The evolution and interaction of non-linear waves in diverse physical systems are described by the KdV equation. The suggested method yields approximate-analytical solutions in the form of a series that are symmetrically dependent on the values of fractional-order derivatives and have simple, understandable mechanics. The Caputo sense of fractional derivative is employed, and the convergence and uniqueness of the methods are analysed. Five test examples are offered to demonstrate the analytical procedure of the technique and it is demonstrated that the proposed techniques are efficient and reduce the number of calculations required. The results obtained from the methods are shown to be in concurrency with exact solutions, and the suggested techniques are deemed powerful for solving non-linear fractional PDEs.

As a result of the study carried out over the previous three decades, fractional calculus has become much more essential due to its broad use in science and engineering. Fractional derivatives and integrals can be used to explain the properties of memory and inheritance. Therefore, there is a growing demand to develop the various numerical methods for solving linear and nonlinear fractional integro-differential equations. In this essay, we reviewed the literature on basic ideas, analytical strategies and several numerical methodologies for solving linear and nonlinear fractional integro differential equations.

In this paper we estimate the maximum number of limit cycles that can bifurcate from an integrable non-linear quadratic ischronous center, when perturbed inside a class of Liénard-like polynomial differential systems of arbitrary degree $n$. The main tool employed in this study is the averaging theory of first order.

Controlling and regulating chaotic dynamics in predator-prey systems have become an attractive field of investigation for researchers in the arena of mathematical biology. We claim Allee effect to be one such measure of controlling chaos in an eco-epidemiological model subject to environmental toxicity. In our investigation, we have established mathematical properties such an existence of points of equilibria and their local stablitiy analysis. Hopf bifurcation analysis have been examined and established followed by permanence of the model taken under consideration. Likewise, we have demonstrated global stability of the interior equilibrium point. Infection parameter $\beta$ and Allee parameter $\theta$ serve the purpose of control parameters. The numerical simulation indicates that with gradual decrease in the value of infection parameter, the system becomes more stable. On the other hand, with increasing value of Allee parameter, the system fetches stability from chaotic behaviour of the system.The analytical findings have been strongly validated by extensive numerical simulation in this article.

Present paper deals with a nutrient-phytoplankton-zooplankton model with viral disease in phytoplankton species. We have considered the stability of different equilibria under some threshold conditions. We have worked out the basic reproduction number and we analyzed the community structure by the help of these basic reproduction number. Our observations indicate that as the parameters cross a certain critical value, then the system enters into Hopf bifurcation so the existence of Hopf-bifurcation for the interior equilibrium of the system is explored. To observe the global behaviour of our model system we have performed extensive numerical simulations. From our numerical results it is clear that viral infection and nutrient concentration are responsible for occurrence and control of phytoplankton blooms. The analysis identifies an important threshold effect: a bloom will only be triggered when nutrients exceed a certain definite level. From our numerical studies we see that viral infection is responsible for zooplankton survival and plankton oscillation dynamics and nutrient threshold is required for plankton oscillations and zooplankton survival.

Defensive behavior is an important factor in changing the system dynamics. Particularly inducible defense in one population may help to persist that population in ecosystem.In this study we analyze a standard model of prey-predator interaction in presence of defensive properties in prey population and also consider the disease infection in predator population.We study local stability, bifurcation of the system around the equilibria and also derive ecological and disease basic reproduction number.The main aim of this work is to study the consequence of the defensive behavior on the model system in presence of disease in predator.Our findings show that defensive behavior in one population stabilizing the infected system contradicting the previous result suggesting destabilizing effect of disease infection.We have done extensive numerical studies to conclude that increasing defensive behavior actually stabilizing the system more rapidly.

The remaining Useful Life (RUL) forecast for rolling bearings is still a crucial part of condition-based maintenance (CBM) for mechanical systems. To predict the RUL, the existing research utilized traditional Deep Learning techniques, however, it has trouble quantifying uncertainty. Therefore, this research suggested a novel deep learning (DL) model to improve RUL prediction. Initially, to define the degree of rolling bearing deterioration and comprehend the non-linear qualities, time domain features, frequency domain features, and time-frequency domain features are removed. Then, this study suggested using a Bi-LSTM - RF framework to predict the RUL, this framework has an LSTM layer in a combination of forward and backward motion, a fully connected layer, an RF classifier, and a dropout layer. As a result, our proposed deep learning-based RUL prediction obtains the Accuracy of 0.9845, Precision of 0.93, Recall of 1.0, and F1-score of 0.9656.

A similarity solution for cylindrically converging shock waves of symmetric flow in MHD propagating into a medium, plasma governed by the equation of state (EOS) of Mie-Gr$\ddot{u}$neisen type, is calculated. The governing equations of flow with total energy and constant specific heats are considered in the Eulerian form. These equations are reduced to a system of differential equations of Poincare type using similarity transformations. The transformed system is then reduced to a finite difference system of equations and solved numerically using MATLAB. In the present work, different non-ideal EOS of Mie-Gr$\ddot{u}$neisen type are considered with suitable material constants. Similarity exponent $\alpha$, which varies with the measure of shock strength, $\beta$ for the considered EOS are evaluated. It is observed that the measure of shock strength $\beta$ affects the shock front. Further, the effect of non-idealness parameters, magnetic field strength on the flow variables are presented.

Tri-trophic food chains represent intricate ecological systems, wherein predators, prey, and primary producers engage in complex interactions. Studying the dynamics of such systems is of paramount importance for understanding the delicate balance of ecosystems and their responses to external perturbations. In this paper, we delve into the intricate dynamics of a tri-trophic food chain model, incorporating the influential Holling Type II functional response, insights from the Hasting and Powell model, and the inclusion of prey and intermediate predator harvesting effects. By analyzing equilibrium points, assessing local and global stability, exploring Hopf bifurcations, chaotic, limit cycle, stability, period-doubling and conducting numerical simulations, we aim to unravel the rich dynamics that arise from these ecological interactions.

The worldwide rapid outbreak of coronavirus disease 2019 (COVID-19) has created a crisis in almost every country. The control of this disease possesses the ultimate challenge throughout the world. The mathematical model is an essential tool to study disease dynamics and is used to understand the impact of several control measures on disease propagation. In this work, we proposed and analyzed a compartmental model to study the spread of COVID-19 and its various control measures. The model parameters are influenced through different precautionary measures such as, social distancing, public awareness, improvement of hospital facilities, rapid case detection through testing, etc. These epidemiologically controllable parameters are directly linked with the disease spreading. Using partial rank correlation coefficient technique we observed that home isolations, self-awareness and social distancing measures have the most positive impact on the basic reproduction number $(R_0)$. An effective control strategy of the disease spread can be implemented through these measures and in some special situations, the value of $R_0$ is less than $1$ i.e. the disease can be controlled if the proper measures are implemented. Moreover, we observed that the recruitment rate plays a vital role in the long-term dynamics and due to the effect of recruitment, there may be a second peak or, the disease may co-exist in the population in absence of vaccination.