Analytical Findings Research Articles

Spatiotemporal dynamics of prey-predator model incorporating Holling-type II functional response with fear and its carryover effects.

The recent focus in the fields of biology and ecology has centered on the significant attention given to the mathematical modeling and analyzing the spatiotemporal population distribution among species engaged in interactions. This paper explores the dynamics of the temporal and spatiotemporal delayed Bazykin-type prey-predator model, incorporating fear and its carryover effect. In our model, we incorporated a functional response of the Holling-type II. In the temporal model, a detailed dynamic analysis was carried out, investigating the positivity and boundedness of solutions, establishing the uniqueness and existence of positive interior equilibria, and examining both local and global stability. Additionally, we explored the presence of saddle-node, transcritical, and Hopf bifurcations varying attack rate parameter. The delayed system shows highly periodic behavior. Additionally, for the spatiotemporal model, we provide a complete analysis of local and global stability, and we derive the conditions for the existence of Turing instability for both self-diffusion and cross-diffusion, respectively. The two-dimensional diffusive model is further discussed, highlighting various Turing patterns, including holes, stripes, and hot and cold spots, along with their biological significance. Numerical simulations are executed to validate the analytical findings in both temporal and spatiotemporal models.

Playing to learn? Analyzing participants' framing of competition and professional conduct in maritime simulations

This study scrutinizes how a simulated scenario framed as a competition is discussed in a post-simulation debriefing, where students reflect on game-like play in the context of professional education. This study draws on Erwin Goffman's (1974/86) analytical concept of framing. In particular, the analysis focuses on the instructor's and students' authentic conversations during a debriefing session and explores how these conversations open up negotiations of professional and playful learning. The research design is ethnographically informed and based on observations, field notes, and 34 h of video data from a navigation course in which 35 bachelor's students from a Norwegian university participated. Our analytical findings reveal that the activity undergoes continuous negotiation between two framings: professional and competitive. In professional framing, students are held accountable for adhering to professional rules, regulations, and norms of “good seamanship.” In the competition framing, students were competing to win the race. Moreover, as the competition mode intensified, students prioritized winning the race over adhering to the rules and regulations of the profession. Consequently, the findings illustrate how a competition framing within a professional education context has engaged the students, letting them demonstrate their knowledge and skills in a playful manner. Furthermore, the findings emphasize the need for an additional exploration of the opportunities and challenges of competition on professional decision making and ethical conduct in settings where simulation-based learning is utilized for training, particularly in domains that train students in high safety standards.

Characteristics of Eco-Friendly Marker Ink by Utilizing Natural Dyes From Noni Leaf Extract (Morinda Citrifolia L.)

Marker ink created from natural ingredients can be used as an alternative to ink with high VOC (Volatile Organic Compound) levels, which can be harmful to one's health. Noni leaf extract includes tannins, which can be utilized as a basic dye/pigment in marker ink. The goal of this study is to use natural dyes derived from noni leaf extract as a replacement for synthetic ink VOC and as an innovation in green marker ink. The study was undertaken with various adjustments, including the inclusion of noni leaf tannins (0.6 gr, 0.8 gr, 1.0 gr, 1.2 gr, 1.4 gr) and gum arabic (4 gr, 5 gr). The analytical findings of the best arker ink products are presented in formula 5, which includes tannins mass 1.4 gr and gum arabic mass 4 gr, with a viscosity of 3.1 cp, density of 1.14 g/ml, pH 6, and concentrated pigment production. Based on these findings, marker ink products fulfill the quality standards of the SNI 06-1567-1999 test.

Computational modelling of cylindrical-ferroelectric-dual metal-nanowire field effect transistor (C-FE-DM-NW FET) using landau equation for gate leakage minimization

In order to address and resolve the significant problem of gate-induced drain leakage (GIDL) current and enhance device reliability, band-to-band tunnelling (BTBT), and OFF-state leakages, a computational model of a cylindrical-ferroelectric-dual-metal-nanowire-field effect transistor (C-FE-DM-NW-FET) has been proposed in this manuscript. The proffered structure is a symmetric gate structure with ferroelectric layer sandwiched between the gate terminal and oxide layer which reduces the BTBT which in term reduces the OFF-state leakage hence making the device definitive for low power applications. In this manuscript, there has been a reduction in the leakage current by a magnitude of 104 times in 50 nm and 107 times in 60 nm channel length which translates to a reduction in gate leakage (IGIDL) of more than 100 % in C-FE-NW-FET over C-NW FET. To analyze the Electric Field, Surface Potential, and IGIDL with the proper boundary conditions, the 2D Poisson's equation is solved analytically with Landau-Khalatnikov (LK) equation. The analytical findings are quite similar to the simulated outcomes.

A robust beamforming with antenna selection approach for dense antenna arrays under limited CSI

This paper introduces a novel approach for dense antenna arrays, which integrates beamforming and antenna selection. The proposed method aims to optimize the number of transmit antennas to reduce power consumption and enhance spectral efficiency at the transmitter. By employing optimal beamforming weights, our approach steers signals toward the intended receiver to maximize the transmit power of the desired signal while mitigating side-lobe interference under channel uncertainty. To adapt beamforming parameters dynamically to changing channel conditions, we develop a channel estimation approach that obtains accurate channel state information (CSI). In contrast to prior studies, our channel estimation method utilizes a generalized Gaussian distribution (GGD) model, capable of accommodating both matched and mismatched CSI features by modeling heavy-tailed and light-tailed distributions. This allows our method to capture diverse channel statistical behaviors resulting from phenomena such as fading and interference under various propagation conditions. Furthermore, we introduce an angle entropy metric, which measures angle of departure (AoD) variations, indicating the degree of uncertainty regarding the directionality of transmitted signals. Simulation results validate the accuracy of our analytical findings and demonstrate the superior performance of the proposed approach in terms of robustness and bit-error-rate (BER) performance.

Performance analysis of two-way multi-users cooperative communication system based on GSPIM-DCSK scheme

Based on the Joint Grouping Subcarrier-Permutation Index Modulation-DCSK (GSPIM-DCSK) system, we provide a new two-way multi-user half-duplex cooperative communication system in this work. Given its many benefits, the GSPIM-DCSK modulation is specifically selected as a choice for network coding techniques. A permutation index is used in the GSPIM-DCSK system to incorporate additional data bits with the modulating and carrier index bits. Establishing a cooperative multiuser system where users attempt to make contact with one another over a common relay is the main goal of this effort. Multi-user nodes and a single relay with a cooperative operator on staff for decoding and forwarding make up this system. To avoid interference from other users, the user’s nodes multiplex across various time intervals. We derive analytical expressions for the average bit error rate (BER) of the GSPIM-DCSK multi-user cooperative communication system in the presence of additive white Gaussian noise (AWGN) and multiple paths Rayleigh fading channels. The analytical and simulated average BER findings have been contrasted to verify the accurateness of the average BER analysis. Additionally, a comparison is presented between the average bit error rate (BER) performance of a novel GSPIM-DCSK cooperative system and an established DCSK cooperative system. The throughput and link spectral efficiency of this novel cooperative system are analyzed and compared with those of existing traditional cooperative systems. For the two-way two-user cooperative system, this comparison is done with two-way two-user systems like DCSK-CC and one-way cooperative system based on CIM-SR-DCSK-CC; for the two-way three-user cooperative system, it is done with scheme1 and scheme2. To compare and assess the performance of various systems, simulation results are employed. Furthermore, an analysis demonstrates how the proposed cooperative system, when combined with GSPIM-DCSK techniques, improves the efficiency of conventional cooperative DCSK systems.

Pilot and data power optimization problems in multiple Aerial Relay Stations cell‐free communication systems

SummaryA cell‐free (CF) technology and unmanned aerial vehicles (UAVs) acting as aerial relay stations (ARSs) are gradually viewed as viable technologies for usage in sixth‐generation (6G) wireless networks owing to their outstanding advantages, such as large coverage, uniform service quality, huge connections, flexible deployment in all geographical areas, and high line‐of‐sight (LoS) probability. As a result, the combination of the CF model and UAVs is suitable for densely populated urban areas, shopping malls, festivals, and locations with complex geography. Furthermore, the integration of the CF model and UAV communication can improve system quality and is considered an entirely new research direction as there is no comprehensive investigation of this combined model. In this study, we investigate the quality of the multi‐ARS CF communication system, where ARSs are equipped with multiple antennas and stochastic distribution within a specific region to simultaneously serve numerous ground users. We establish a closed‐form formulation for the uplink and downlink throughput of individual users by using the matched filtering method and conjugate beamforming technology, respectively. Moreover, we propose a novel method to optimize the pilot and data transmission power coefficients for improving channel estimation and increasing throughput per user, thereby ensuring a high quality of service. The power optimization method is executed via the successive convex approximation (SCA) method, second‐order cone program (SOCP), and linear program. We evaluate system performance according to the cumulative distribution function (CDF) of user throughput based on various parameters, such as the number of users, the number of ARSs, and the length of pilot sequences. The analytical findings also reveal that the system with the proposed power optimization method is always superior to the system without the proposed method in both uplink and downlink.

Dynamics of a discrete one‐predator two‐prey system with Michaelis–Menten‐type prey harvesting and prey refuge

In this paper, we propose and study a discretized one‐predator two‐prey system along with prey refuge and Michaelis–Menten‐type prey harvesting. The interaction among the species is considered as Holling type III functional response. Firstly, existence and local stability of all the fixed points are derived under certain parametric conditions. Furthermore, a special consideration is made to global asymptotic stability of the interior fixed point. Then, we have shown that the system undergoes different types of bifurcations including transcritical bifurcation, flip bifurcation, and Neimark–Sacker bifurcation by using center manifold theorem, bifurcation theory, and normal form method. Also, Feigenbaum's constant of the system is calculated. It is observed that both harvesting and refuge have a stabilizing effect on the system, and the stabilizing effect of harvesting dominates the stabilizing effect of refuge. Of most interest is the finding of coexisting attractors and multistability. In particular, optimal harvesting policy has been obtained by extension of Pontryagin's maximum principle to discrete system. Finally, some intriguing numerical simulations are provided to verify our analytic findings and rich dynamics of the three species system.

Effect of Horizontal Distance of Web Opening on the Ultimate Load Carrying Capacity of Castellated Steel Beams by an Analytical Approach

Objectives: The primary objective of this current research is to determine the ideal horizontal spacing for hexagonal web openings and their maximum load-bearing capacity through Finite Element Analysis (FEA). Methods: The ISMB150 was implemented as a cross-sectional profile to fabricate distinct models of castellated beams with heights of 225 mm. The height of the web openings remained constant at 150 mm for the castellated beam model. The entire analysis is being done on ANSYS 19.2. Findings: The analysis has revealed that, for castellated beams with shallower depths, an optimal horizontal spacing of 44.9 mm for the web openings yields an ultimate load-bearing capacity of 144.26 KN. The results of castellated beams are measured in terms of ultimate load-carrying capacity, span-to-deflection ratio, load density, failure location, span-to-beam depth ratio, and the ratio of horizontal distance of opening-to-opening depth. Novelty: This research contributes analytical findings for the ideal horizontal distance of hexagonal web opening through maximum load-bearing capacity. Castellated beams have gained immense popularity within the structural engineering community today due to their visually appealing design featuring a variety of web-opening shapes. The primary objective of this current research is to determine the ideal horizontal spacing for hexagonal web openings and their maximum load-bearing capacity through Finite Element Analysis (FEA). The ISMB150 was implemented as a cross-sectional profile to fabricate distinct models of castellated beams with heights of 225 mm. The height of the web openings remained constant at 150 mm for the castellated beam model. The analysis has revealed that, for castellated beams with shallower depths, an optimal horizontal spacing of 44.9 mm for the web openings yields an ultimate load-bearing capacity of 144.26 KN. The results of castellated beams are measured in terms of ultimate load-carrying capacity, span-to-deflection ratio, load density, failure location, span-to-beam depth ratio, and the ratio of horizontal distance of opening-to-opening depth. This research contributes valuable insights into optimizing the design of castellated beams for enhanced structural performance. Further exploration and validation could provide additional refinements and applications in structural engineering. Keywords: Horizontal distance of web opening, Number of openings, Ultimate load carrying capacity, Failure modes, ANSYS, Castellated beams

Global Properties of a Discrete SARS-CoV-2/HIV Co-Dynamics Model

Coronavirus disease 2019 (COVID-19), which is caused by the virus known as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), is a respiratory disease. In this paper, we analyze the global stability of a discrete SARS-CoV-2/HIV co-dynamics model. We create the discrete model by applying a nonstandard finite difference (NSFD) method. We demonstrate that NSFD retains essential solution properties, including positivity and boundedness. We determine the fixed points and identify their existence conditions. We investigate the global stability of these fixed points through the application of the Lyapunov method. To complement our analytical findings, we present numerical simulations.

The Stability of Solutions of the Variable-Order Fractional Optimal Control Model for the COVID-19 Epidemic in Discrete Time

This article introduces a discrete-time fractional variable order over a SEIQR model, incorporated for COVID-19. Initially, we establish the well-possedness of solution. Further, the disease-free and the endemic equilibrium points are determined. Moreover, the local asymptotic stability of the model is analyzed. We develop a novel discrete fractional optimal control problem tailored for COVID-19, utilizing a discrete mathematical model featuring a variable order fractional derivative. Finally, we validate the reliability of these analytical findings through numerical simulations and offer insights from a biological perspective.

New results on positive almost periodicity of some proportional delayed SICNNs involving D operator

In this paper, we first substantiate the global existence of bounded positive solutions for a kind of shunting inhibitory cellular neural networks with D operator and proportional delay. Second, by utilising differential inequality techniques and the Lyapunov functional method, some testable criteria are achieved to verify the global exponential stability of the positive almost periodic solutions for the proposed networks, which encompasses existing ones in the literature as some special cases. Finally, an explanatory example is performed to justify our analytical findings.

Does mutual interference stabilize prey–predator model with Bazykin–Crowley–Martin trophic function?

We investigated a system of ordinary differential equations that describes the dynamics of prey and predator populations, taking into account the Allee effect affecting the reproduction of the predator population, and mutual interference amongst predators, which is modeled with the Bazykin–Crowley–Martin (BCM) trophic function. Bifurcation analysis revealed a rich spectrum of bifurcations occurring in the system. In particular, analytical conditions for the saddle–node, Hopf, cusp, and Bogdanov–Takens bifurcations were derived for the model parameters, quantifying the strength of the predator interference, the Allee effect, and the predation efficiency. Numerical simulations verify and illustrate the analytical findings. The main purpose of the study was to test whether the mutual interference in the model with BCM trophic function provides a stabilizing or destabilizing effect on the system dynamics. The obtained results suggest that the model demonstrates qualitatively the same pattern concerning varying the interference strength as other predator-dependent models: both low and very high interference levels increase the risk of predator extinction, while moderate interference has a favorable effect on the stability and resilience of the prey–predator system.

Analyzing the dynamic patterns of COVID-19 through nonstandard finite difference scheme

This paper presents a novel approach to analyzing the dynamics of COVID-19 using nonstandard finite difference (NSFD) schemes. Our model incorporates both asymptomatic and symptomatic infected individuals, allowing for a more comprehensive understanding of the epidemic's spread. We introduce an unconditionally stable NSFD system that eliminates the need for traditional Runge–Kutta methods, ensuring dynamical consistency and numerical accuracy. Through rigorous numerical analysis, we evaluate the performance of different NSFD strategies and validate our analytical findings. Our work demonstrates the benefits of using NSFD schemes for modeling infectious diseases, offering advantages in terms of stability and efficiency. We further illustrate the dynamic behavior of COVID-19 under various conditions using numerical simulations. The results from these simulations demonstrate the effectiveness of the proposed approach in capturing the epidemic's complex dynamics.

Analysis of Prey-Predator Scheme in Conjunction with Help and Gestation Delay

This paper presents a three-dimensional continuous time dynamical system of three species, two of which are competing preys and one is a predator. We also assume that during predation, the members of both teams of preys help each other and the rate of predation of both teams is different. The interaction between prey and predator is assumed to be governed by a Holling type II functional response and discrete type gestation delay of the predator for consumption of the prey. In this work, we establish the local asymptotic stability of various equilibrium points to understand the dynamics of the model system. Different conditions for the coexistence of equilibrium solutions are discussed. Persistence, permanence of the system, and global stability of the positive interior equilibrium solution are discussed by constructing suitable Lyapunov functions when the gestation delay is zero, and there is no periodic orbit within the interior of the first quadrant of state space around the interior equilibrium. As we introduced time delay due to the gestation of the predator, we also discuss the stability of the delayed model. It is observed that the existence of stability switching occurs around the interior equilibrium point as the gestation delay increases through a certain critical threshold. Here, a phenomenon of Hopf bifurcation occurs, and a stable limit cycle corresponding to the periodic solution of the system is also observed. This study reveals that the delay is taken as a bifurcation parameter and also plays a significant role for the stability of the proposed model. Computer simulations of numerical examples are given to explain our proposed model. We have also addressed critically the biological implications of our analytical findings with proper numerical examples.

Highly dispersive optical solitons with differential group delay for Sasa-Satsuma equation having multiplicative white noise

AbstractThis paper is about the retrieval of highly dispersive optical solitons for Sasa-Satsuma equation with differential group delay in presence of white noise. There are four integration schemes that make this retrieval possible. A full spectrum of optical solitons have been revealed from these schemes. The parametric restrictions for the existence of such solitons are also presented. The displayed surface plots support the analytical findings.

Linguistic tone in Chinese rap: an interdisciplinary approach

This study, integrating linguistics, computer science, statistics, musicology, and cultural study, explores how the lexical tones of Mandarin Chinese interact with rap music. We develop an algorithm to compute the Tonal Congruence Index (ITG ), measuring the extent to which tones are preserved in vocal music. Analysis of a dataset with over 8000 syllables from Mandarin Chinese rap songs shows that the tonal congruence is related to subgenres that have evolved over time: while tones are largely preserved in the earlier boom-bap style, tonal distortion occurs more frequently in recent trap music. Moreover, we find that the falling fourth tone in standard Mandarin accounts for 38% of line-ending syllables in the lyrics of 140 rap songs and further suggests that the pre-eminence of the fourth tone may be a generic feature of Mandarin Chinese rap, particularly in boom bap. In addition, Chinese rappers have increasingly utilised English words over time to achieve musical flow. Integrating analytic findings with qualitative interviews of five national award-winning Chinese rappers, we conclude that the restriction of linguistic tones in Mandarin Chinese rap has gradually weakened over time and that there is a decreasing correlation between tone and rap with the emergence of new rap styles such as mumble rap and melodic rap.

Adaptive bipartite output containment control of heterogeneous multi‐agent systems against FDI attacks

AbstractThis paper researches the adaptive bipartite output containment control of heterogeneous multi‐agent systems (HMASs) against false data injection (FDI) attacks. The malicious adversaries could inject attacks on the actuator to maximize damage to the HMASs, which in turn causes the compromised followers to be unable to track the output states of the leaders. To address this issue, a resilient layer is introduced that prevents attack signals from affecting the states. Moreover, an adaptive compensator is ingeniously devised to counteract these attacks, thereby ensuring that both cooperative and antagonistic agents adhere to distinct convex hulls. Leveraging the output regulation approach, conducting Lyapunov stability analysis, and drawing upon other pertinent methodologies, we have systematically constructed a robust framework for the realization of bipartite output containment control. Ultimately, the validity of the analytical findings is confirmed through a series of rigorous numerical simulations.

Performance analysis of 5G and beyond mixed THz/FSO relaying communication systems

This paper explores the potential of relay-assisted transmission to mitigate fading in free-space optical (FSO) systems. Our investigation focuses on assessing the performance of a dual-hop relay system for Terahertz/FSO (THz/FSO) communication. We develop an aggregated channel model incorporating various factors, including pointing errors, channel fading, and deterministic path loss. Specifically, the THz link encounters α−μ fading with pointing errors, while the FSO link experiences Gamma–Gamma fading and pointing errors. We utilize amplify-and-forward relaying and derive mathematical expressions for the probability density function and cumulative distribution function of the end-to-end signal-to-noise ratio, considering the combined effects of channel fading and pointing errors. Employing the derived statistical expressions, we evaluate crucial performance metrics for the considered relaying schemes, including the outage probability and the average bit error rate. To validate our analytical findings, we conducted Monte-Carlo simulations. The results demonstrate a strong correlation between the performance of the system and the particular pointing errors and fading parameters linked to the THz/FSO connections.

Long-term equilibrium in electricity markets with renewables and energy storage only

AbstractIn this paper, we study the optimal generation mix in power systems where only two technologies are available: variable renewable energy (VRE) and electric energy storage (EES). By using a net load duration curve approach, we formulate a least-cost optimization model in which EES is only limited by its power capacity. We solve this problem analytically and find least-cost and market equilibrium conditions that lead to the optimal capacities of VRE and EES. We show that, mathematically, an electricity price structure that depends on the period of the year (i.e. EES charging or discharging, VRE curtailment, load shedding) and on investments costs leads to cost recovery for VRE and EES. We show that when EES is the marginal technology (either charging or discharging) the price must be non-zero. More specifically, the equilibrium prices during EES charge or discharge are functions of the EES and VRE fixed costs. We confirm our analytical findings using a numerical model. We argue that, although the system we study is hypothetical and simplified, our findings provide insights and research directions for how to recover fixed costs in a future electricity market based on VRE and EES only.