Ramsaday College

This paper proposes a fractional-order seven-compartmental model including five human compartments and two vector compartments to describe the transmission dynamics of dengue disease. We take into account the saturated treatment function while forming the model, incorporating three controls: awareness control, treatment control, and insecticide control. The intricate dynamics of the system, encompassing the existence and uniqueness of solutions as well as their biological feasibility, are thoroughly examined. The threshold parameter of the system, known as the basic reproduction number, is derived, along with the conditions for the occurrence of backward bifurcation and transcritical bifurcation. We also acquired the equilibria and their stability in relation to variations in the basic reproduction number. Furthermore, we have demonstrated that both backward and transcritical bifurcations can be influenced simply by adjusting the cure rate efficiency and the potency of insecticide controls, which remain within our sphere of control. The analytical result is verified through some numerical work. Finally, we apply the genetic algorithm optimization technique, which is independent of the initial state of the population, to minimize the basic reproduction number by optimizing three control parameters and the cure rate. Optimizing the control parameters and cure rate, we have deduced that the disease will die out in the case of transcritical bifurcation, but it will remain in the population in an equilibrium state for the backward bifurcation.

This study presents the formulation of a spatiotemporal eco-epidemic model that takes into account an infectious disease affecting the prey population incorporating prey refugees and intraspecific competition of predators. In this work, we mainly focus on the interior equilibrium, which exists depending on the values of system parameters. In the absence of diffusion, our system shows rich dynamics, like Hopf bifurcation, chaos, etc. We analytically investigate the potential conditions for Turing instability in the context of diffusion. During numerical verification of our theoretical results, we see some non-stationary patterns along with the stationary pattern. By obtaining the Maximum Lyapunov exponent, we confirmed that the non-stationary pattern is chaotic. In addition, it is to be noted that maintaining ecosystem stability, preventing unpredictable population fluctuations, and ensuring the sustainability of species and resources all depend on controlling chaos in ecological models. For this purpose, we apply time-delay feedback control and successfully stabilize the spatiotemporal chaos.

This paper focuses on an incommensurate fractional-order bidirectional associative memory neural network (BAMNN) with leakage and axonal delays, comprising eight neurons. Conditions on the occurrence of Hopf bifurcation have been proposed for both systems (those with and without leakage delay), taking time delay as the bifurcation parameter. The impact of time delay on both systems is illustrated numerically. We have shown that time delays tend to destabilize the system. Furthermore, we have observed that the Hopf bifurcation occurs earlier in the BAMNN with leakage delay than in the BAMNN without leakage delay. Finally, we have shown that for both systems, the fractional order is inversely related to the threshold time delay for Hopf bifurcation events.

We report high-resolution Monte Carlo evidence characterizing the hierarchy of transition strengths in biaxial nematogens. By employing multiple histogram reweighting on large lattices, we demonstrate that while the isotropic-to-uniaxial (I → N_U) transition is symmetry-enforced first-order, the uniaxial-to-biaxial (N_U → N_B) transition in the region between the tricritical point and the triple point (λ= 0.26) is proximity-driven and more than an order of magnitude smaller for large system sizes. Such a class of ultra-weak first-order transitions could be a new pathway for future investigations.

Studying phylogenetic trees can help us understand the evolution of present-day species. By analysing these trees, we can compare different species of animals and gain a better understanding of how they have evolved. We can also learn about major changes in evolution, such as the rise of new body plans or metabolism, the origin of new genes, molecular adaptation, morphological character evolution, and demographic changes in recently diverged species. Various types of algorithms exists for constructing phylogenetic trees. In this article, we have taken a closer look at four of these algorithms, which can be categorized into two types on the basis of the method used: distance-based and character-based. Furthermore, we have also delved into the numerous applications of phylogenetic trees, as they serve a significant purpose in various fields.