Vol. 1 No. 3 (2023)

Applied mathematics plays an important role in ecological research by providing quantitative tools to model, analyze, and understand complex ecological systems. The interdisciplinary nature of applied mathematics in ecological research allows for a deeper understanding of the intricate relationships within ecosystems and aids in addressing pressing environmental challenges. In this issue, we delved into the intersection of applied mathematics and ecology through various research papers. We aim to offer valuable insights into the application of mathematical principles in understanding ecological phenomena.

  • Open Access

    Article

    Article ID: 129

    The study of chaotic dynamics of an eco-epidemiological predator-prey model with alternative food

    by Prodip Roy, Abhishek Sarkar, Kulbhushan Agnihotri, Krishna Pada Das

    Journal of AppliedMath, Vol.1, No.3, 2023; 75 Views, 101 PDF Downloads

    Parasites can alter the quality and quantity of participants. On the other hand, the spread of diseases between individuals or species is an important research topic. Here we consider a tritrophic food model in which bacteria spread among the animal's environment where other nutrients are present. We analyze the local stability of the model around the efficiency of the equation. We also report significant numbers of offspring in terms of ecology and disease and use these numbers to analyze community structure of the sample. We started from this situation as a model. Our numerical results show that at low infection level the body causes conflict, but at high infection level conflict prioritizes safety. Our findings therefore challenge previous models’ predictions that the parasite has a negative impact. We also looked at the impact of other foods on chaotic dynamics. When other nutrients increase, stress does not change, but when other nutrients decrease, chaos disappears and the disease among animals is eliminated from the body.

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  • Open Access

    Article

    Article ID: 194

    Numerical investigation of heat and mass transfer of variable viscosity Casson nanofluid flow through a microchannel filled with a porous medium

    by Lemi Guta Enyadene, Ebba Hindebu Rikitu, Adugna Fita Gabissa

    Journal of AppliedMath, Vol.1, No.3, 2023; 115 Views, 19 PDF Downloads

    Thermal behaviours and hydrodynamics of non-Newtonian nanofluids flow through permeable microchannels have large scale utilizations in industries, engineering, and biomedicine. Therefore, this paper presents the numerical investigation of heat and mass transfer of variable-viscosity Casson nanofluid flow through a porous medium microchannel with the Cattaneo-Christov heat flux theory. The highly nonlinear PDEs corresponding to the continuity, momentum, energy, and concentration equations are formulated and solved numerically via the second-order implicit finite difference scheme known as the Keller-Box method. Accordingly, the numerical simulations reveal that the variable viscosity parameter, thermal Grashof number, solutal Grashof number, thermophoresis parameter, Schmidt number, and Casson fluid parameter show increasing effects on both velocity and temperature of the nanofluid. Furthermore, the temperature profile escalates with increasing values of the Eckert number and the thermal relaxation time parameter. Thus, the Cattaneo-Christov heat flux model is beneficial in warming the transport system of microfluidics when compared to that of the classical Fourier heat conduction law. The temperature profile, however, indicates a retarding behavior with increasing values of the Brownian motion parameter, Prandtl number, and porous medium parameters, namely the Forchheimer number and porous medium shape parameter, and hence, the porous medium quite effectively controls the nanofluid temperature distribution, which plays substantial roles in cooling the transport system of microfluidics. Moreover, the concentration profile shows an increasing pattern with escalating values of the Prandtl number, Schmidt number, and thermophoresis parameter, but it demonstrates a decreasing trend with the Casson fluid, variable viscosity, thermal relaxation time, and solutal relaxation time parameters. It is also observed that the coefficient of skin friction increases with increasing values of the pressure gradient parameter, Eckert number, Forchheimer number, and injection/suction Reynolds number. Besides, the heat transfer rate at both walls of the microchannel increases with rising values of the Eckert number, variable viscosity, parameter, and injection/suction Reynolds number. The Casson fluid and thermal relaxation time parameters reveal opposite scenarios for the heat transfer rate at the left and right walls of the microchannel. In addition the mass transfer rate at both walls of the microchannel shows an increasing pattern as the Eckert number, variable viscosity parameter, Schmidt number, and suction/injection Reynolds number increase.

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  • Open Access

    Article

    Article ID: 199

    The synergistic effect of the multiple parameters of vibro-impact nonlinear energy sink

    by Petro Lizunov, Olga Pogorelova, Tetiana Postnikova

    Journal of AppliedMath, Vol.1, No.3, 2023; 97 Views, 14 PDF Downloads

    This article studies the dynamics and efficiency of a vibro-impact damper (single-sided vibro-impact nonlinear energy sink—SSVI NES) depending on the exciting force parameters. The damper is coupled with a linear oscillator—the primary structure. It is shown that the damper is quite effective in a wide range of the exciting force amplitude and in the range of its frequency, which are higher than the resonant frequency; damper efficiency in these regions is fairly stable. The dynamics of the vibro-impact system “primary structure—SSVI NES” is rich and complex, which, however, does not impair the damper efficiency. In complex oscillatory regimes, the damper makes bilateral impacts: it hits both an obstacle and directly against the primary structure, which actually turns a single-sided NES into a double‐sided one. The optimization procedure and the choice of optimal damper parameters play a very important role in damper design. Optimizing multiple damper parameters instead of three shows a synergistic effect and provides better results.

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  • Open Access

    Article

    Article ID: 303

    Statistical analysis of melody lengths, note probabilities and note transitions of a bandish in raga Bihag

    by Soubhik Chakraborty, Prerna Singh

    Journal of AppliedMath, Vol.1, No.3, 2023; 78 Views, 56 PDF Downloads

    Melody refers to a succession of musical notes that can be regarded as complete in a musical sense. For example, a line of a song or a raga bandish is a melody as it is complete. The number of notes in a melody is called its length. Unfortunately, the analysis of melody lengths is a neglected area in music research. Given that the significance of a melody in monophonic music (single melody line), such as Indian classical music is quantified by the product of the length of the melody and its frequency (number of occurrences in the musical piece), the novelty of our research lies in analysing the statistical features of lengths of a well-known bandish in raga Bihag . Additionally, the probability distribution of the notes is presented and a count of rising and falling note transitions in the sthayi and antara of the bandish is also taken. The experimental results are encouraging.

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  • Open Access

    Article

    Article ID: 246

    Dynamics of insect predator and mosquito prey system with mutual interference as a factor for the co-occurrence: Validating through models

    by Chandrani Mukherjee, Krishna Pada Das, Goutam Panigrahi

    Journal of AppliedMath, Vol.1, No.3, 2023; 94 Views, 78 PDF Downloads

    Several models have been proposed as an extension to the classical Holling’s disc equation to evaluate the predator and prey interactions and their applied aspects in biological control and population regulation of the target organisms. In a one-prey and two-predator dynamic system with mutual interference m as a quadratic parameter of predator density, an evaluation was made of the resultant impact on the prey. A simulation was carried out to see the finite-time extinction of prey and the stability of the system at origin, i.e., when all three species are extinct. We assumed the data obtained was for the interactions between the mosquito and the water bug predators that are common in the freshwater wetlands and involved in population regulation. Despite the benefits to the prey population due to interference and competition, the expected extinction of prey in a finite time is still observed. With varying magnitudes of m, the declining growth curve of the prey population shifted. The equation proposed was also compared with the Crowley-Martin functional response, and considerable differences were observed in selected instances when compared to the growth rate of the predators in a species-specific manner. The stability of the system was deduced from the eigenvalues of the Jacobian matrix at the origin to prove the extinction is stable. Our assessment supports the possible cooccurrence of predators and mosquito prey in the wetlands, with mutual interference being one of the major factors.

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  • Open Access

    Review

    Article ID: 91

    Student satisfaction in higher education: A systematic review examining its impact on institutional growth and comparative dimensions

    by Shahrukh Aman, Nosheen Aziz, Mohsin Abbas

    Journal of AppliedMath, Vol.1, No.3, 2023; 520 Views, 22 PDF Downloads

    The purpose of this comprehensive evaluation of the literature is to examine the connection between higher education institution expansion and student satisfaction (SS). The survey also aims to pinpoint the metrics being contrasted right now when gauging student happiness. The review summarizes recent scholarly publications, including books, conference papers, and journal articles. The results give insight into the comparative dimensions used in student satisfaction research and shed light on the influence of student satisfaction on the growth of higher education institutions.

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