Triveni Devi Bhalotia College

We propose and analyze a three-dimensional eco-epidemiological model involving susceptible and infected prey and predators, in which the predators are supplemented with a constant externally supplied food supply. The model incorporates nonlinear disease transmission and predator feeding saturation through a generalized Holling type II functional response. We investigate the system's dynamics analytically and numerically by examining the existence and stability of equilibria, as well as Hopf, transcritical, and saddle-node bifurcations. One- and two-parameter bifurcation analyses reveal rich dynamics, including limit cycles, period doubling, and chaotic oscillations. Our findings indicate that disease transmission can destabilize the system, while the inclusion of additional food enhances stability and can suppress chaos. Furthermore, we extend the model by introducing a time-dependent optimal control variable representing additional food supply, and derive an optimal strategy using Pontryagin's Maximum Principle. Numerical simulations show that optimal control effectively reduces disease prevalence and stabilizes population dynamics. This study highlights the potential of ecological interventions, such as strategic food supplementation, in regulating complex eco-epidemiological systems.

In this study, an efficient and convenient three component cyclization protocol is presented for the development of synthetically important chromeno[4,3-b]chromene/chromeno[2,3‐d]pyrimidine derivatives via lemon juice mediated reaction of substituted salicylaldehyde, 4-hydroxycoumarin/1,3-dimethylbarbituric acid and electron rich arenes. As lemon juice is cheap, readily accessible, biodegradable, and nontoxic, the present method is environmentally benign and economical. Moreover, our development is simple to handle, produces high yields, tolerates many functional groups, provides easy isolation, and allows for scalable synthesis—all of which align with the basic principles of green chemistry.

Eco-epidemiological systems, in which infectious diseases interact with ecological processes such as predation and competition, exhibit rich and often counterintuitive dynamics. In predator-prey systems, where the prey population is subject to disease, additional ecological mechanisms such as the Allee effect and non-consumptive fear responses can critically influence stability, persistence and extinction outcomes. Furthermore, biological processes like predator gestation introduce time delays that can fundamentally alter system trajectories. In this study, we develop and analyze a nonlinear predatorpreydisease model incorporating (i) a strong Allee effect in the prey population, (ii) fear-mediated reductions in prey growth rates and (iii) an explicit gestation delay in predator reproduction. Analytical investigations are conducted to determine the existence and stability conditions of equilibria, extinction thresholds and bifurcation structures. The delay is treated as a bifurcation parameter to assess its influence on the stability of the coexistence equilibrium and the onset of oscillatory dynamics. Numerical simulations further reveal delay-induced destabilization, bistability and shifts in the basins of attraction. The results highlight how the combined effects of ecological constraints, behavioral adaptations and epidemiological factors shape the qualitative dynamics of eco-epidemiological systems, offering new insights into population persistence and control strategies.

PurposeThe purpose of this study is to investigate the effects of multiplicative noise on the exact solutions of the generalized nonlinear Schr & ouml;dinger equation. By employing two direct methods, we derive precise solutions, including hyperbolic, trigonometric and Jacobi elliptic function solutions. The research aims to enhance understanding of how multiplicative noise influences the behavior of these solutions, providing valuable insights into the dynamics of stochastic systems. Graphical examples illustrate the impact of noise, contributing to the broader field of nonlinear dynamics and its applications in physics and engineering.Design/methodology/approachThis study employs a two-pronged approach to derive exact solutions of the generalized nonlinear Schr & ouml;dinger equation influenced by multiplicative noise. Initially, a similarity transformation reduces the stochastic problem to a second-order cubic nonlinear ordinary differential equation. Subsequently, four mappings between the Riccati equation and the reduced ordinary differential equation are established using the generalized unified method. The solutions generated include hyperbolic, trigonometric and Jacobi elliptic functions. The behavior of these solutions under varying levels of multiplicative noise is analyzed, supported by graphical representations to illustrate the effects of noise on the derived solutions.FindingsThe findings reveal that multiplicative noise significantly affects the exact solutions of the generalized nonlinear Schr & ouml;dinger equation. The study successfully derives multiple families of solutions, including hyperbolic, trigonometric and Jacobi elliptic functions, demonstrating the versatility of the employed methods. The analysis shows that the introduction of noise alters the stability and dynamics of these solutions, leading to complex behaviors. Graphical examples illustrate the impact of varying noise levels, highlighting the importance of considering stochastic effects in nonlinear systems. These results contribute to a deeper understanding of noise-induced phenomena in mathematical physics and engineering applications.Originality/valueThis study offers original contributions by exploring the effects of multiplicative noise on the exact solutions of the generalized nonlinear Schr & ouml;dinger equation, an area that has received limited attention in existing literature. By employing innovative methods, including the generalized unified technique and Jacobi elliptic function method, the research generates a diverse set of solutions that enhance the understanding of stochastic dynamics in nonlinear systems. The findings provide valuable insights into the interplay between noise and soliton behavior, which can inform future research and applications in fields such as optics, plasma physics and complex systems.

This study addresses the critical need to enhance heat and mass transport in nanofluid-based biotechnological and biomedical systems through bioconvective mechanisms. The aim is to investigate magneto-bioconvective flow of a Williamson nanofluid containing gyrotactic microorganisms over a flexible cylinder embedded in a Darcy-Forchheimer porous medium. The model incorporates thermal radiation, Arrhenius activation energy, Brownian motion, thermophoresis, and wall slip effects to capture realistic transport physics. Governing partial differential equations were transformed into ordinary differential equations via similarity variables and solved numerically using MATHEMATICA 10. Results demonstrate that thermal radiation and thermophoresis elevate temperature distributions, whereas increased Williamson fluid parameter, Forchheimer number, porosity, and magnetic field strength suppress velocity and concentration profiles. Sensitivity analysis further reveals that thermophoresis significantly enhances heat transfer while the Lewis number critically controls microorganism distribution, offering actionable insights for optimizing nanofluid applications in energy and biomedical engineering.